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229.65 530.47 Tm ({P} )Tj /T1_0 1 Tf 0 Tc 10.1 0 0 10.1 249.99 530.47 Tm (x )Tj 0.05 Tc 10.4517 0 0 9.8 258.32 530.47 Tm (ps )Tj 0.0324 Tc 9.4 0 0 9.4 272.14 530.47 Tm (vanishes. )Tj 0.0394 Tc -25.24 -1.264 Td (First )Tj 0.0421 Tc 2.426 0 Td (assume )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 92.1 518.59 Tm (r )Tj /T1_0 1 Tf 13.9 0 0 13.9 100.19 518.59 Tm (= )Tj /T1_2 1 Tf 9 0 0 9 111.31 518.59 Tm (1 )Tj /T1_0 1 Tf 0.05 Tc 9.4 0 0 9.4 119.42 518.59 Tm (and )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 138.5 518.59 Tm (F )Tj /T1_0 1 Tf 0.05 Tc 9.4344 0 0 9.4 149.57 518.59 Tm (not )Tj 0.0051 Tc 9.4 0 0 9.4 166.77 518.59 Tm (does )Tj 0.0238 Tc 2.306 0 Td (not )Tj 0.0116 Tc 1.761 0 Td (vanish )Tj 0.0353 Tc 3.114 0 Td (on )Tj /T1_1 1 Tf 0.05 Tc 10.2174 0 0 9.6 248.43 518.59 Tm (X. )Tj /T1_0 1 Tf 9.7761 0 0 9.4 265.09 518.59 Tm (Let )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 283.67 518.59 Tm (S )Tj /T1_0 1 Tf 0.05 Tc 9.7011 0 0 9.4 293.77 518.59 Tm (be )Tj 9.8357 0 0 9.4 307.6 518.59 Tm (the )Tj 0.0233 Tc 9.4 0 0 9.4 324.59 518.59 Tm (subvariety )Tj -0.0032 Tc -32.319 -1.226 Td (defined )Tj -0.0138 Tc 3.553 0 Td (by )Tj /T1_1 1 Tf 0.05 Tc 9.82 0 0 9.6 68.66 507.0699 Tm (F. )Tj /T1_0 1 Tf -0.0198 Tc 9.4 0 0 9.4 87.81 507.0699 Tm (We )Tj 0.0045 Tc 1.936 0 Td (have )Tj 0.0104 Tc 2.438 0 Td (seen )Tj 0.05 Tc 10.0691 0 0 9.4 151 507.0699 Tm (that )Tj 9.5625 0 0 9.4 172.78 507.0699 Tm (the )Tj 0.0152 Tc 9.4 0 0 9.4 190.43 507.0699 Tm (hypersurface )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 246.41 507.0699 Tm (S )Tj /T1_2 1 Tf 11.2 0 0 11.2 255.2 507.0699 Tm (n )Tj 9.5 0 0 9.5 264.77 507.0699 Tm (X )Tj /T1_0 1 Tf 0.0491 Tc 9.4 0 0 9.4 278.73 507.0699 Tm (of )Tj /T1_2 1 Tf 0 Tc 9.5 0 0 9.5 291.23 507.0699 Tm (X )Tj /T1_0 1 Tf 0.0334 Tc 9.4 0 0 9.4 305.01 507.0699 Tm (contains )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 343.92 507.0699 Tm (q )Tj /T1_2 1 Tf 12.3 0 0 12.3 351.34 507.0699 Tm (+ )Tj 9.5 0 0 9.5 361.85 507.0699 Tm (1 )Tj /T1_0 1 Tf 0.0166 Tc 9.4 0 0 9.4 21.05 495.55 Tm (hypersurfaces )Tj 0.05 Tc 9.8076 0 0 9.4 78.93 495.55 Tm (of )Tj 0.0466 Tc 9.4 0 0 9.4 90.7 495.55 Tm (type )Tj /T1_1 1 Tf 0.0408 Tc 10.5 0 0 10.5 112.11 495.55 Tm ({P} )Tj /T1_0 1 Tf 0 Tc 10.9 0 0 10.9 132.08 495.55 Tm (x )Tj 0.05 Tc 10.8388 0 0 9.8 140.6 495.55 Tm (ps )Tj 0.0286 Tc 9.4 0 0 9.4 154.79 495.55 Tm (with )Tj /T1_1 1 Tf 0 Tc 10.5 0 0 10.5 176.3 495.55 Tm (P )Tj /T1_2 1 Tf 8.3 0 0 8.3 186.29 495.55 Tm (E )Tj /T1_0 1 Tf 0.05 Tc 11.1214 0 0 9.8 194.96 495.55 Tm (pr )Tj /T1_2 1 Tf -0.0139 Tc 9.8 0 0 9.8 205.93 495.55 Tm (\(F )Tj /T1_0 1 Tf -0.035 Tc 9.5134 0 0 10.3 215.55 495.55 Tm (q\). )Tj 0.0113 Tc 9.4 0 0 9.4 230.54 495.55 Tm (Hence )Tj /T1_2 1 Tf 0.05 Tc 11.3709 0 0 9.3 258.39 495.55 Tm (FIX )Tj /T1_0 1 Tf 0.0276 Tc 9.4 0 0 9.4 281.14 495.55 Tm (vanishes, )Tj -0.0167 Tc 4.357 0 Td (as )Tj 0.0208 Tc 1.178 0 Td (wanted. )Tj -0.035 Tc 9.3057 0 0 9.4 34.96 483.67 Tm (Now, )Tj 0.0459 Tc 9.4 0 0 9.4 58.76 483.67 Tm (assume )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 93 483.67 Tm (r )Tj /T1_2 1 Tf 11.1 0 0 11.1 101.16 483.67 Tm (> )Tj /T1_0 1 Tf -0.035 Tc 8.9497 0 0 9.5 111.83 483.67 Tm (1. )Tj 0.0237 Tc 9.4 0 0 9.4 124.52 483.67 Tm (By )Tj 0.0377 Tc 1.623 0 Td (induction )Tj -0.003 Tc 4.48 0 Td (on )Tj /T1_1 1 Tf -0.035 Tc 9.8548 0 0 10 195.24 483.67 Tm (r, )Tj /T1_0 1 Tf 8.7957 0 0 9.4 205.55 483.67 Tm (we )Tj -0.0121 Tc 9.4 0 0 9.4 219.29 483.67 Tm (see )Tj 0.05 Tc 10.1785 0 0 9.4 235.24 483.67 Tm (that )Tj -0.0277 Tc 9.4 0 0 9.4 256.04 483.67 Tm (for )Tj 0.039 Tc 1.551 0 Td (every )Tj 0.0434 Tc 2.844 0 Td (hyperplane )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 346.93 483.67 Tm (H )Tj /T1_0 1 Tf 0.0108 Tc 9.4 0 0 9.4 358.83 483.67 Tm (of )Tj 0.05 Tc 11.5333 0 0 9.8 21.08 472.5099 Tm (pr )Tj 0 Tc 9.4 0 0 9.4 34.65 472.5099 Tm (defined )Tj 0.0148 Tc 3.389 0 Td (over )Tj /T1_2 1 Tf 0 Tc 9.3 0 0 9.3 87.26 472.5099 Tm (F )Tj /T1_0 1 Tf 0.05 Tc 7.9767 0 0 6.2 94.43 472.5099 Tm (q, )Tj 9.6991 0 0 9.4 104.74 472.5099 Tm (the )Tj 0.0315 Tc 9.4 0 0 9.4 120.97 472.5099 Tm (polynomial )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 169.82 472.5099 Tm (F )Tj /T1_0 1 Tf 0.0016 Tc 9.4 0 0 9.4 179.8 472.5099 Tm (vanishes )Tj -0.003 Tc 3.822 0 Td (on )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 228.68 472.5099 Tm (H )Tj /T1_2 1 Tf 9.1 0 0 9.1 240.29 472.5099 Tm (x )Tj /T1_0 1 Tf 0.05 Tc 9.9513 0 0 9.8 248.78 472.5099 Tm (ps. )Tj 9.8977 0 0 9.4 265.96 472.5099 Tm (This )Tj 0.0361 Tc 9.4 0 0 9.4 288.46 472.5099 Tm (implies )Tj 0.05 Tc 9.8502 0 0 9.4 321.46 472.5099 Tm (that )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 341.8 472.5099 Tm (S )Tj /T1_2 1 Tf 10.8 0 0 10.8 349.71 472.5099 Tm (n )Tj /T1_1 1 Tf 9.9 0 0 9.9 358.22 472.5099 Tm (X )Tj /T1_0 1 Tf -0.035 Tc 9.0754 0 0 9.4 20.99 460.63 Tm (is )Tj 0.0238 Tc 9.4 0 0 9.4 30.41 460.63 Tm (not )Tj 0 Tc 1.714 0 Td (a )Tj 0.0361 Tc 0.833 0 Td (hypersurface )Tj 0.0491 Tc 5.947 0 Td (of )Tj 0.05 Tc 10.2724 0 0 10 120.94 460.63 Tm (X, )Tj 10.2879 0 0 9.4 135.33 460.63 Tm (that )Tj -0.0179 Tc 9.4 0 0 9.4 155.98 460.63 Tm (is )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 165.86 460.63 Tm (F )Tj /T1_0 1 Tf 0.0044 Tc 9.4 0 0 9.4 175.84 460.63 Tm (vanishes )Tj 0.0161 Tc 3.822 0 Td (on )Tj /T1_1 1 Tf 0.05 Tc 10.589 0 0 10 225.04 460.63 Tm (X. )Tj /T1_0 1 Tf 0 Tc 8.1 0 0 8.1 359.92 460.63 Tm (0 )Tj -0.035 Tc 9.1049 0 0 9.4 34.71 449.2899 Tm (We )Tj 0.0294 Tc 9.4 0 0 9.4 50.49 449.2899 Tm (conclude )Tj 0.0432 Tc 4.239 0 Td (this )Tj 0.0242 Tc 1.941 0 Td (section )Tj 0.0478 Tc 3.364 0 Td (with )Tj 0.0422 Tc 2.316 0 Td (the )Tj 0.0021 Tc 1.678 0 Td (case )Tj 0.0108 Tc 2.087 0 Td (of )Tj 0.0269 Tc 1.118 0 Td (minimal )Tj 0.0094 Tc 3.861 0 Td (degree )Tj 0.0221 Tc 3.117 0 Td (scrolls. )Tj 0.05 Tc 10.5051 0 0 9.4 20.97 427.5099 Tm (Theorem )Tj 10.142 0 0 9.5 66 427.5099 Tm (2.3 )Tj /T1_1 1 Tf 0.0135 Tc 9.9 0 0 9.9 85.58 427.5099 Tm (Fix )Tj -0.0031 Tc 1.643 0 Td (positive )Tj -0.0079 Tc 3.391 0 Td (integers )Tj -0.035 Tc 8.9958 0 0 9.9 169.51 427.5099 Tm (q, )Tj -0.0123 Tc 9.9 0 0 9.9 179.8 427.5099 Tm (k, )Tj 0.05 Tc 10.6294 0 0 9.9 190.38 427.5099 Tm (nand )Tj /T1_0 1 Tf 0.0306 Tc 9.4 0 0 9.4 215.62 427.5099 Tm (m, )Tj /T1_1 1 Tf -0.0075 Tc 9.9 0 0 9.9 229.81 427.5099 Tm (with )Tj /T1_0 1 Tf 0 Tc 9.4 0 0 9.4 249.46 427.5099 Tm (m )Tj 11.2 0 0 11.2 260.58 427.5099 Tm (< )Tj /T1_1 1 Tf 0.05 Tc 10.565 0 0 9.6 269.94 427.5099 Tm (n, )Tj 12.2639 0 0 9.9 282.53 427.5099 Tm (\(n-m+ )Tj 0.0388 Tc 9.9 0 0 9.9 319.06 427.5099 Tm (I\)k )Tj /T1_0 1 Tf -0.035 Tc 8.3621 0 0 9.9 334.59 427.5099 Tm (::; )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 344.64 427.5099 Tm (q )Tj -0.0274 Tc 0.782 0 Td (and )Tj 0 Tc -33.491 -1.164 Td [(q )-141(a )]TJ -0.0262 Tc 1.658 0 Td (power )Tj 0.05 Tc 10.2615 0 0 9.9 64.53 415.99 Tm (of )Tj 0 Tc 9.9 0 0 9.9 76.26 415.99 Tm (a )Tj 0.0097 Tc 0.821 0 Td (prime. )Tj 0.0076 Tc 3.286 0 Td (Let )Tj 0 Tc 1.646 0 Td (X )Tj /T1_2 1 Tf 7.8001 0 0 7.8001 145.15 415.99 Tm (C )Tj 0.05 Tc 9.8748 0 0 9.1 155.51 415.99 Tm (pn )Tj /T1_1 1 Tf -0.035 Tc 8.3188 0 0 9.9 171.84 415.99 Tm (be )Tj 0 Tc 9.9 0 0 9.9 183.54 415.99 Tm (a )Tj 0.0261 Tc 0.783 0 Td (m-dimensional )Tj -0.0094 Tc 6.593 0 Td (irreducible )Tj 0.0028 Tc 4.789 0 Td (non-degenerate )Tj -0.0093 Tc -28.546 -1.2 Td (variety )Tj 0.0431 Tc 3.107 0 Td (of )Tj 0.0389 Tc 1.094 0 Td (minimal )Tj -0.035 Tc 9.3536 0 0 9.9 101.29 404.11 Tm (degree )Tj -0.002 Tc 9.9 0 0 9.9 129.4 404.11 Tm (\(that )Tj -0.035 Tc 9.7704 0 0 9.9 152.34 404.11 Tm (is, )Tj -0.0257 Tc 9.9 0 0 9.9 165.37 404.11 Tm (with )Tj -0.035 Tc 9.0019 0 0 9.9 185.71 404.11 Tm (degree )Tj 0 Tc 9.9 0 0 9.9 212.17 404.11 Tm (n )Tj /T1_0 1 Tf 0.793 0 Td (-)Tj /T1_2 1 Tf 8.6 0 0 8.6 228.97 404.11 Tm (m )Tj 12.9 0 0 12.9 239.55 404.11 Tm (+ )Tj /T1_0 1 Tf -0.0236 Tc 10 0 0 10 249.31 404.11 Tm (1\) )Tj /T1_1 1 Tf -0.0079 Tc 9.9 0 0 9.9 261.49 404.11 Tm (defined )Tj 0.015 Tc 3.306 0 Td (over )Tj /T1_0 1 Tf 0 Tc 10 0 0 10 315.32 404.11 Tm (F )Tj /T1_2 1 Tf 0.05 Tc 8.012 0 0 6 321.94 404.11 Tm (q' )Tj /T1_1 1 Tf 0.0042 Tc 9.9 0 0 9.9 334.6 404.11 Tm (Then )Tj /T1_3 1 Tf 0 Tc 9.5 0 0 9.5 358.12 404.11 Tm (X )Tj /T1_1 1 Tf -0.013 Tc 9.9 0 0 9.9 21.27 392.59 Tm (satisfies )Tj 0.05 Tc 10.7516 0 0 9.9 55.7 392.59 Tm (FFN\(k,q\). )Tj /T1_0 1 Tf 0.0065 Tc 9.4 0 0 9.4 21.02 370.81 Tm (Proof. )Tj /T1_2 1 Tf 0.05 Tc 12.1279 0 0 9.3 60.51 370.81 Tm (If )Tj /T1_0 1 Tf 0 Tc 9.4 0 0 9.4 70.9 370.81 Tm (m )Tj 13.2 0 0 13.2 83.27 370.81 Tm (= )Tj -0.0275 Tc 9.4 0 0 9.4 95.07 370.81 Tm (1, )Tj 0.05 Tc 9.5414 0 0 9.4 106 370.81 Tm (then )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 128.54 370.81 Tm (X )Tj /T1_0 1 Tf -0.0179 Tc 9.4 0 0 9.4 140.5 370.81 Tm (is )Tj 0 Tc 1.089 0 Td (a )Tj 0.0321 Tc 0.91 0 Td (normal )Tj 0.0294 Tc 3.428 0 Td (rational )Tj 0.0295 Tc 3.668 0 Td (curve )Tj 0.0308 Tc 2.776 0 Td (and )Tj 0.05 Tc 10.1089 0 0 9.4 270.7 370.81 Tm (the )Tj 9.4058 0 0 9.4 288.53 370.81 Tm (result )Tj -0.0178 Tc 9.4 0 0 9.4 316.16 370.81 Tm (follows )Tj -0.0094 Tc 3.351 0 Td (from )Tj 0.0241 Tc -34.753 -1.245 Td (Theorem )Tj -0.0022 Tc 4.138 0 Td (2.2. )Tj 0.0082 Tc -2.657 -1.206 Td (Assume )Tj 0 Tc 3.696 0 Td (m )Tj /C0_0 1 Tf 6.3001 0 0 7.3801 82.45 347.77 Tm <007E0020>Tj /T1_0 1 Tf -0.035 Tc 8.5333 0 0 9.4 93.73 347.77 Tm (2. )Tj 0.05 Tc 9.7534 0 0 9.4 106.49 347.77 Tm (If )Tj 0 Tc 9.4 0 0 9.4 116.62 347.77 Tm (X )Tj -0.0179 Tc 1.296 0 Td (is )Tj 0.05 Tc 9.5655 0 0 9.4 138.77 347.77 Tm (not )Tj 0.0337 Tc 9.4 0 0 9.4 156.11 347.77 Tm (smooth, )Tj 0.0402 Tc 3.841 0 Td (then )Tj 0.05 Tc 9.4923 0 0 9.4 213.58 347.77 Tm (it )Tj -0.035 Tc 9.3682 0 0 9.4 223.3 347.77 Tm (is )Tj 0 Tc 9.4 0 0 9.4 233.36 347.77 Tm (a )Tj 0.0036 Tc 0.901 0 Td (cone )Tj 0.0223 Tc 2.372 0 Td (\(defined )Tj 0.0212 Tc 3.985 0 Td (over )Tj 0 Tc 2.265 0 Td (F )Tj -0.035 Tc 8.6824 0 0 10.3 329.5 347.77 Tm (q\) )Tj -0.0043 Tc 9.4 0 0 9.4 341.19 347.77 Tm (over )Tj 0 Tc 2.201 0 Td (a )Tj -0.0288 Tc -36.266 -1.226 Td (lower )Tj 0.0392 Tc 2.546 0 Td (dimensional )Tj 0.05 Tc 9.4326 0 0 9.4 97.79 336.25 Tm (smooth )Tj 0.0397 Tc 9.4 0 0 9.4 131.56 336.25 Tm (minimal )Tj 0.0094 Tc 3.918 0 Td (degree )Tj 0.0011 Tc 3.09 0 Td (variety, )Tj 0.0264 Tc 3.454 0 Td (say )Tj -0.0072 Tc 1.812 0 Td (Y, )Tj 0.05 Tc 9.5177 0 0 9.4 259.97 336.25 Tm (spanning )Tj 9.8357 0 0 9.4 301.48 336.25 Tm (the )Tj 0.0233 Tc 9.4 0 0 9.4 318.52 336.25 Tm (linear )Tj 0.0071 Tc 2.771 0 Td (space )Tj /T1_3 1 Tf 0.05 Tc 9.8041 0 0 9.8 20.94 324.7299 Tm (M, )Tj /T1_0 1 Tf 0.0286 Tc 9.4 0 0 9.4 35.81 324.7299 Tm (with )Tj /T1_1 1 Tf 0.05 Tc 13.7303 0 0 9.9 56.09 324.7299 Tm (n-m )Tj /T1_2 1 Tf 0 Tc 9.9 0 0 9.9 81.92 324.7299 Tm (= )Tj /T1_0 1 Tf 0.0413 Tc 9.4 0 0 9.4 92.25 324.7299 Tm (dim )Tj /T1_3 1 Tf 0.05 Tc 11.8135 0 0 9.8 110.77 324.7299 Tm (\(M\)-)Tj /T1_0 1 Tf 9.5198 0 0 9.4 137.79 324.7299 Tm (dim )Tj /T1_3 1 Tf 0.005 Tc 9.8 0 0 9.8 156.54 324.7299 Tm (\(Y\) )Tj /T1_2 1 Tf 0.05 Tc 11.397 0 0 9 171.98 324.7299 Tm (-1, )Tj /T1_0 1 Tf 0.0404 Tc 9.4 0 0 9.4 189.62 324.7299 Tm (and )Tj 0.0286 Tc 1.81 0 Td (with )Tj 0.0216 Tc 2.173 0 Td (as )Tj 0.0304 Tc 1.157 0 Td (vertex )Tj 0 Tc 2.94 0 Td (a )Tj 0.05 Tc 9.4029 0 0 9.4 272.98 324.7299 Tm (linear )Tj 9.4035 0 0 9.4 299.21 324.7299 Tm (space )Tj /T1_3 1 Tf -0.0328 Tc 9.8 0 0 9.8 324.54 324.7299 Tm (V, )Tj /T1_0 1 Tf 0.0064 Tc 9.4 0 0 9.4 337.05 324.7299 Tm (defined )Tj -0.0171 Tc -33.645 -1.264 Td (over )Tj 0 Tc 2.054 0 Td (F )Tj 0.05 Tc 7.9767 0 0 6.5001 46.73 312.85 Tm (q, )Tj 9.4612 0 0 9.4 56.69 312.85 Tm (with )Tj 9.8481 0 0 9.4 78.21 312.85 Tm (dim )Tj /T1_3 1 Tf -0.025 Tc 10.4 0 0 10.4 97.84 312.85 Tm (\(V\) )Tj /T1_0 1 Tf 0 Tc 13.9 0 0 13.9 115.49 312.85 Tm (= )Tj /T1_2 1 Tf 0.05 Tc 12.3844 0 0 8.6 125.04 312.85 Tm (m-)Tj /T1_0 1 Tf 9.4104 0 0 9.4 143.73 312.85 Tm (dim )Tj /T1_3 1 Tf -0.0337 Tc 10.4 0 0 10.4 163 312.85 Tm (\(Y\) )Tj /T1_0 1 Tf 0.05 Tc 12.5799 0 0 9.5 179.31 312.85 Tm (-1. )Tj 0.0194 Tc 9.4 0 0 9.4 198.82 312.85 Tm (Taking )Tj 0 Tc 3.272 0 Td (a )Tj 0.0348 Tc 0.787 0 Td (linear )Tj 0.0491 Tc 2.733 0 Td (subspace )Tj 0.0376 Tc 4.313 0 Td (complementary )Tj 0.0488 Tc -30.037 -1.226 Td (to )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 32.06 301.33 Tm (V )Tj /T1_0 1 Tf 0.05 Tc 9.4 0 0 9.4 42.38 301.33 Tm (and )Tj 0.0288 Tc 1.916 0 Td (defined )Tj -0.0043 Tc 3.581 0 Td (over )Tj 0 Tc 2.15 0 Td (F )Tj 0.05 Tc 8.2046 0 0 6.5001 120.88 301.33 Tm (q, )Tj -0.035 Tc 9.1156 0 0 9.4 131.21 301.33 Tm (we )Tj 0.023 Tc 9.4 0 0 9.4 145.25 301.33 Tm (reduce )Tj 0.05 Tc 9.6041 0 0 9.4 175.12 301.33 Tm (to )Tj 0.0231 Tc 9.4 0 0 9.4 186.64 301.33 Tm (the )Tj 0.0021 Tc 1.639 0 Td (case )Tj 0.0051 Tc 2.088 0 Td (in )Tj 0.013 Tc 1.156 0 Td (which )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 259.83 301.33 Tm (X )Tj /T1_0 1 Tf 0.0395 Tc 9.4 0 0 9.4 271.36 301.33 Tm (is )Tj 0.05 Tc 9.499 0 0 9.4 281.39 301.33 Tm (smooth. )Tj 0.0219 Tc 9.4 0 0 9.4 35.06 289.63 Tm (Fix )Tj 0 Tc 1.717 0 Td (a )Tj 0.0285 Tc 0.805 0 Td (degree )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 89.26 289.63 Tm (k )Tj /T1_0 1 Tf 0.0235 Tc 9.4 0 0 9.4 97.55 289.63 Tm (homogeneous )Tj 0.0187 Tc 6.168 0 Td (polynomial )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 203.48 289.63 Tm (F )Tj /T1_0 1 Tf 0.0248 Tc 9.4 0 0 9.4 213.46 289.63 Tm (vanishing )Tj -0.003 Tc 4.416 0 Td (on )Tj 0 Tc 1.367 0 Td (X )Tj 0.05 Tc 10.1729 0 0 9.4 277.62 289.63 Tm (\(F )Tj -0.035 Tc 9.8724 0 0 10.6 287.73 289.63 Tm (q\). )Tj 0.0235 Tc 9.4 0 0 9.4 303.28 289.63 Tm (Assume )Tj 0 Tc 3.715 0 Td (m )Tj /T1_2 1 Tf 8.6 0 0 8.6 349.24 289.63 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 8.7919 0 0 9.4 359.23 289.63 Tm (2, )Tj 0.0404 Tc 9.4 0 0 9.4 20.96 277.9299 Tm (and )Tj 0.0273 Tc 1.904 0 Td (take )Tj 0 Tc 2.117 0 Td (a )Tj 0.0498 Tc 0.852 0 Td (hyperplane )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 116.54 277.9299 Tm (H )Tj /T1_0 1 Tf 0.0128 Tc 9.4 0 0 9.4 127.89 277.9299 Tm (defined )Tj -0.0043 Tc 3.466 0 Td (over )Tj 0 Tc 2.15 0 Td (F )Tj /T1_2 1 Tf 0.05 Tc 8.012 0 0 6 187.12 277.9299 Tm (q' )Tj /T1_0 1 Tf 0.0393 Tc 9.4 0 0 9.4 34.87 266.59 Tm (Either )Tj 0 Tc 3.01 0 Td (X )Tj /T1_2 1 Tf 11.2 0 0 11.2 74.3 266.59 Tm (n )Tj /T1_3 1 Tf 9.5 0 0 9.5 83.23 266.59 Tm (H )Tj /T1_0 1 Tf -0.0179 Tc 9.4 0 0 9.4 95.5 266.59 Tm (is )Tj 0 Tc 1.032 0 Td (a )Tj 0.0398 Tc 0.871 0 Td (normal )Tj 0.0485 Tc 3.389 0 Td (rational )Tj 0.0008 Tc 3.745 0 Td (curve )Tj 0.0351 Tc 2.619 0 Td (spanning )Tj /T1_3 1 Tf 0 Tc 9.5 0 0 9.5 244.87 266.59 Tm (H )Tj /T1_0 1 Tf 0.03 Tc 9.4 0 0 9.4 256.41 266.59 Tm (or )Tj 0 Tc 1.252 0 Td (X )Tj /T1_2 1 Tf 11.2 0 0 11.2 279.5 266.59 Tm (n )Tj /T1_3 1 Tf 9.5 0 0 9.5 288.43 266.59 Tm (H )Tj /T1_0 1 Tf 0.0012 Tc 9.4 0 0 9.4 300.52 266.59 Tm (is )Tj 0 Tc 1.07 0 Td (a )Tj 0.0299 Tc 0.89 0 Td (nodal )Tj 0.0056 Tc 2.73 0 Td (curve )Tj -0.0062 Tc -34.44 -1.226 Td (which )Tj -0.035 Tc 9.3682 0 0 9.4 47.08 255.0699 Tm (is )Tj 0.0437 Tc 9.4 0 0 9.4 56.34 255.0699 Tm (union )Tj 0.05 Tc 10.0163 0 0 9.4 82.88 255.0699 Tm (of )Tj 0 Tc 9.4 0 0 9.4 94.22 255.0699 Tm (a )Tj 0.0103 Tc 0.826 0 Td (line )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 119.97 255.0699 Tm (D )Tj /T1_0 1 Tf 0.05 Tc 9.5174 0 0 9.4 130.94 255.0699 Tm (and )Tj 0 Tc 9.4 0 0 9.4 149.3 255.0699 Tm (a )Tj 0.0359 Tc 0.833 0 Td (normal )Tj 0.0321 Tc 3.351 0 Td (rational )Tj 0.0199 Tc 3.63 0 Td (curve )Tj 0 Tc 2.699 0 Td (C )Tj 0.05 Tc 9.4719 0 0 9.4 258.17 255.0699 Tm (spanning )Tj 0 Tc 9.4 0 0 9.4 299.06 255.0699 Tm (a )Tj 0.037 Tc 0.871 0 Td (hyperplane )Tj /T1_1 1 Tf 0.0127 Tc 9.9 0 0 9.9 355.76 255.0699 Tm (H' )Tj /T1_0 1 Tf -0.0083 Tc 9.4 0 0 9.4 20.97 243.3699 Tm (of )Tj /T1_3 1 Tf 0.05 Tc 9.4624 0 0 9.3 31.39 243.3699 Tm (H, )Tj /T1_0 1 Tf 0.0414 Tc 9.4 0 0 9.4 45.17 243.3699 Tm (with )Tj /T1_2 1 Tf -0.0318 Tc 12.3 0 0 12.3 66.98 243.3699 Tm (Ie )Tj /T1_0 1 Tf 0 Tc 12.9 0 0 12.9 79.36 243.3699 Tm (n )Tj /T1_3 1 Tf -0.035 Tc 10.2559 0 0 12.9 88.25 243.3699 Tm (DI )Tj /T1_2 1 Tf 0 Tc 9.3 0 0 9.3 101.91 243.3699 Tm (= )Tj /T1_0 1 Tf -0.035 Tc 9.2294 0 0 9.4 112.18 243.3699 Tm (1. )Tj /T1_2 1 Tf 0.05 Tc 11.4723 0 0 9.3 34.42 232.03 Tm (If )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 43.65 232.03 Tm (X )Tj /T1_2 1 Tf 10.8 0 0 10.8 53.25 232.03 Tm (n )Tj /T1_3 1 Tf 9.3 0 0 9.3 60.91 232.03 Tm (H )Tj /T1_0 1 Tf 0.0012 Tc 9.4 0 0 9.4 72.46 232.03 Tm (is )Tj 0.05 Tc 9.4471 0 0 9.4 81.77 232.03 Tm (smooth, )Tj -0.035 Tc 9.1156 0 0 9.4 118.25 232.03 Tm (we )Tj 0.0109 Tc 9.4 0 0 9.4 131.93 232.03 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0.0318 Tc 0.995 0 Td (divided )Tj 0.0053 Tc 3.572 0 Td (by )Tj 0.0422 Tc 1.376 0 Td (the )Tj 0.0272 Tc 1.669 0 Td (polynomial )Tj 0.0207 Tc 5.14 0 Td (defining )Tj /T1_3 1 Tf 0.05 Tc 9.8065 0 0 9.3 283.56 220.69 Tm (H. )Tj /T1_0 1 Tf -0.035 Tc 9.1049 0 0 9.4 34.71 208.81 Tm (We )Tj 0.0197 Tc 9.4 0 0 9.4 50.67 208.81 Tm (could )Tj 0.0116 Tc 2.7 0 Td (check )Tj 0.0334 Tc 2.815 0 Td (directly )Tj 0.05 Tc 10.1785 0 0 9.4 137.14 208.81 Tm (that )Tj /T1_3 1 Tf 10.418 0 0 9.8 157.9 208.81 Tm (FIH )Tj /T1_2 1 Tf -0.035 Tc 5.9049 0 0 11.8 179.37 208.81 Tm (== )Tj /T1_0 1 Tf 0 Tc 9.4 0 0 9.4 189.62 208.81 Tm (0 )Tj -0.0157 Tc 0.804 0 Td (even )Tj 0.0189 Tc 2.262 0 Td (if )Tj 0 Tc 0.906 0 Td (X )Tj /T1_2 1 Tf 11.2 0 0 11.2 237.92 208.81 Tm (n )Tj /T1_3 1 Tf 9.5 0 0 9.5 247.03 208.81 Tm (H )Tj /T1_0 1 Tf -0.035 Tc 9.0754 0 0 9.4 258.59 208.81 Tm (is )Tj 0.0459 Tc 9.4 0 0 9.4 267.89 208.81 Tm (singular, )Tj 0.05 Tc 10.0045 0 0 9.4 308.17 208.81 Tm (but )Tj -0.035 Tc 8.9557 0 0 9.4 325.61 208.81 Tm 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70.7 185.95 Tm (n )Tj /T1_3 1 Tf 9.5 0 0 9.5 79.81 185.95 Tm (H )Tj /T1_0 1 Tf 0.0337 Tc 9.4 0 0 9.4 92.03 185.95 Tm (smooth. )Tj -0.035 Tc 9.3057 0 0 9.4 34.96 174.25 Tm (Now, )Tj 0.0498 Tc 9.4 0 0 9.4 59.3 174.25 Tm (assume )Tj 0 Tc 3.666 0 Td (m )Tj /T1_2 1 Tf 11.5 0 0 11.5 106.38 174.25 Tm (> )Tj /T1_0 1 Tf 9.4 0 0 9.4 117.3 174.25 Tm (2 )Tj 0.05 Tc 9.5174 0 0 9.4 125.9 174.25 Tm (and )Tj 9.5625 0 0 9.4 145.06 174.25 Tm (the )Tj 0.0312 Tc 9.4 0 0 9.4 161.99 174.25 Tm (result )Tj 0.0384 Tc 2.852 0 Td (true )Tj -0.0277 Tc 2.117 0 Td (for )Tj -0.0048 Tc 1.591 0 Td (lower )Tj 0.0354 Tc 2.718 0 Td (dimensional )Tj 0.0397 Tc 5.695 0 Td (minimal )Tj 0.0056 Tc 3.995 0 Td (degree )Tj 0.0077 Tc -33.982 -1.245 Td (varieties. )Tj 0.0496 Tc 4.631 0 Td (Let )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 83.05 162.55 Tm (H )Tj /T1_0 1 Tf 0.0432 Tc 9.4 0 0 9.4 96.67 162.55 Tm (be )Tj 0 Tc 1.482 0 Td (a )Tj 0.0413 Tc 0.967 0 Td (hyperplane )Tj 0.0032 Tc 5.277 0 Td (defined )Tj -0.0107 Tc 3.523 0 Td (over )Tj 0 Tc 2.246 0 Td (F )Tj /T1_2 1 Tf 0.05 Tc 8.2477 0 0 6 230.14 162.55 Tm (q' )Tj 11.4723 0 0 9.3 245.2 162.55 Tm (It )Tj /T1_0 1 Tf -0.0082 Tc 9.4 0 0 9.4 256.76 162.55 Tm (follows )Tj 0.05 Tc 10.5068 0 0 9.4 289.59 162.55 Tm (that )Tj 0 Tc 9.4 0 0 9.4 312.1 162.55 Tm (X )Tj /T1_2 1 Tf 11.2 0 0 11.2 323.78 162.55 Tm (n )Tj /T1_3 1 Tf 9.3 0 0 9.3 333.07 162.55 Tm (H )Tj /T1_0 1 Tf -0.035 Tc 9.3682 0 0 9.4 346.06 162.55 Tm (is )Tj 0.0447 Tc 9.4 0 0 9.4 356.48 162.55 Tm (an )Tj 0.0171 Tc -35.692 -1.206 Td (irreducible )Tj 0.05 Tc 9.7801 0 0 9.4 67.38 151.21 Tm (\(m )Tj 0 Tc 9.4 0 0 9.4 81.61 151.21 Tm (-)Tj 0.05 Tc 9.4181 0 0 9.4 91.91 151.21 Tm (I\)-dimensional )Tj 0.0301 Tc 9.4 0 0 9.4 156.76 151.21 Tm (minimal )Tj 0.0017 Tc 3.841 0 Td (degree )Tj 0.0276 Tc 3.04 0 Td (subvariety )Tj 0.05 Tc 9.5989 0 0 9.4 266.31 151.21 Tm (of )Tj /T1_3 1 Tf 9.8065 0 0 9.3 277.8 151.21 Tm (H. )Tj /T1_0 1 Tf -0.0103 Tc 9.4 0 0 9.4 34.88 139.69 Tm (Hence, )Tj /T1_3 1 Tf 0.05 Tc 10.8389 0 0 9.3 64.84 139.69 Tm (FIH )Tj /T1_2 1 Tf -0.035 Tc 6.0689 0 0 11.8 87.2 139.69 Tm (== )Tj /T1_0 1 Tf 0 Tc 9.4 0 0 9.4 97.28 139.69 Tm (0 )Tj 0.0245 Tc 0.854 0 Td (by )Tj 0.05 Tc 9.5625 0 0 9.4 118.42 139.69 Tm (the )Tj 0.0329 Tc 9.4 0 0 9.4 134.56 139.69 Tm (inductive )Tj 0.0151 Tc 4.373 0 Td (hypothesis, )Tj 0.05 Tc 5.103 0 Td (and )Tj -0.035 Tc 9.1156 0 0 9.4 241.91 139.69 Tm (we )Tj 0.05 Tc 9.6384 0 0 9.4 255.69 139.69 Tm (obtain )Tj 9.4901 0 0 9.4 285.74 139.69 Tm (again )Tj /T1_3 1 Tf 0 Tc 9.3 0 0 9.3 311.82 139.69 Tm (F )Tj /T1_2 1 Tf 1.119 0 Td (= )Tj /T1_0 1 Tf -0.035 Tc 6.6904 0 0 9.4 331.85 139.69 Tm (O. )Tj 0 Tc 14 0 0 14 21.25 107.83 Tm (3 )Tj 0.05 Tc 15.0454 0 0 14 44.01 107.83 Tm (Linearly )Tj 15.4452 0 0 14 106 107.83 Tm (normal )Tj 15.3422 0 0 14 159.08 107.83 Tm (smooth )Tj 14.7783 0 0 14 213.33 107.83 Tm (curves )Tj 0.0051 Tc 9.4 0 0 9.4 21.17 86.58 Tm (In )Tj 0.0146 Tc 1.219 0 Td (section )Tj -0.035 Tc 9.3091 0 0 9.4 64.03 86.58 Tm (2, )Tj 9.2755 0 0 9.4 74.87 86.58 Tm (we )Tj 0.0256 Tc 9.4 0 0 9.4 89.55 86.58 Tm (considered )Tj 0.05 Tc 9.5625 0 0 9.4 136.06 86.58 Tm (the )Tj 0.0085 Tc 9.4 0 0 9.4 152.55 86.58 Tm (case )Tj 0.03 Tc 2.126 0 Td (of )Tj -0.0101 Tc 1.156 0 Td (Veronese )Tj 0.0295 Tc 4.109 0 Td (embeddings )Tj 0.05 Tc 9.8076 0 0 9.4 273.51 86.58 Tm (of )Tj /T1_2 1 Tf 9.8497 0 0 9.3 284.93 86.58 Tm (pm )Tj /T1_0 1 Tf 9.8699 0 0 9.4 303.2 86.58 Tm (and )Tj 0.03 Tc 9.4 0 0 9.4 322.11 86.58 Tm (of )Tj 0.0136 Tc 1.156 0 Td (varieties )Tj 0.0252 Tc -33.193 -1.205 Td (containing )Tj 0.05 Tc 9.7399 0 0 9.4 66.04 75.25 Tm (many )Tj 0.001 Tc 9.4 0 0 9.4 92.8 75.25 Tm (lines. )Tj 0.0051 Tc -6.165 -1.245 Td (In )Tj 0.0432 Tc 1.193 0 Td (this )Tj 0.0397 Tc 1.903 0 Td (section, )Tj -0.035 Tc 9.1156 0 0 9.4 99.17 63.55 Tm (we )Tj -0.0055 Tc 9.4 0 0 9.4 113.03 63.55 Tm (will )Tj 0.0254 Tc 1.887 0 Td (consider )Tj 0.05 Tc 9.4259 0 0 9.4 167.38 63.55 Tm (the )Tj -0.0107 Tc 9.4 0 0 9.4 183.33 63.55 Tm (case )Tj 0.0108 Tc 2.049 0 Td (of )Tj 0.0089 Tc 1.091 0 Td (curves, )Tj 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)Tj 0.0498 Tc 0.788 0 Td (hyperplanes )Tj 0.0022 Tc 5.682 0 Td (defined )Tj -0.011 Tc 3.368 0 Td (over )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 23.9 540.37 Tm (F )Tj /T1_0 1 Tf 0.05 Tc 8.4326 0 0 6.2 30.7 540.37 Tm (q, )Tj 9.9723 0 0 9.3 41.38 540.37 Tm (the )Tj 9.3212 0 0 9.3 58.33 540.37 Tm (property )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 96.92 540.37 Tm [(F )116(F )96(N )]TJ -0.019 Tc 2.39 0 Td (\(k, )Tj -0.035 Tc 8.732 0 0 9.3 133.15 540.37 Tm (q\) )Tj /T1_0 1 Tf -0.0305 Tc 9.3 0 0 9.3 144.28 540.37 Tm (is )Tj -0.0164 Tc 1.004 0 Td (false )Tj -0.012 Tc 2.206 0 Td (for )Tj 0.0163 Tc 1.529 0 Td (every )Tj 0.0413 Tc 2.702 0 Td (proper )Tj 0.05 Tc 9.34 0 0 9.3 243.05 540.37 Tm (subvariety )Tj /T1_1 1 Tf 10.589 0 0 9.9 290.02 540.37 Tm (X, )Tj /T1_0 1 Tf 0.0255 Tc 9.3 0 0 9.3 303.94 540.37 Tm (if )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 312.64 540.37 Tm (k )Tj /C0_0 1 Tf 5.5801 0 0 7.2001 320.77 540.37 Tm <007E0020>Tj /T1_1 1 Tf 9.3 0 0 9.3 329.88 540.37 Tm (q )Tj /T1_2 1 Tf 12.7 0 0 12.7 336.57 540.37 Tm (+ )Tj -0.035 Tc 7.6019 0 0 9.2 346.26 540.37 Tm (1. )Tj /T1_0 1 Tf 0.05 Tc 10.0089 0 0 9.3 38.25 528.85 Tm (The )Tj 9.3212 0 0 9.3 58.51 528.85 Tm (property )Tj /T1_1 1 Tf 10.5296 0 0 9.9 97.28 528.85 Tm (FFN\(k,q\) )Tj /T1_0 1 Tf -0.0305 Tc 9.3 0 0 9.3 144.82 528.85 Tm (is )Tj 0.0444 Tc 1.032 0 Td (true )Tj 0.0449 Tc 2.084 0 Td (if )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 182.72 528.85 Tm (X )Tj /T1_0 1 Tf -0.0111 Tc 9.3 0 0 9.3 194.14 528.85 Tm (is )Tj 0 Tc 1.044 0 Td (a )Tj 0.0305 Tc 0.882 0 Td (projective )Tj 0.05 Tc 9.3282 0 0 9.3 255.29 528.85 Tm (space )Tj 0.0384 Tc 9.3 0 0 9.3 281.96 528.85 Tm (embedded )Tj 0.0307 Tc 4.762 0 Td (as )Tj 0 Tc 1.258 0 Td (a )Tj 0.0246 Tc 0.833 0 Td (linear )Tj 0.0302 Tc -34.631 -1.277 Td (space, )Tj -0.0055 Tc 3.058 0 Td (see )Tj -0.035 Tc 8.6539 0 0 10.9 68.01 516.97 Tm ([6, )Tj 0.0135 Tc 9.3 0 0 9.3 80.77 516.97 Tm (Ex. )Tj -0.035 Tc 9.3417 0 0 10.9 99.22 516.97 Tm (1.1] )Tj 0.05 Tc 9.3999 0 0 9.3 116.9 516.97 Tm (and )Tj 0.0044 Tc 9.3 0 0 9.3 135.17 516.97 Tm (references )Tj 0.033 Tc 4.547 0 Td (therein. )Tj 0.05 Tc 9.8989 0 0 9.3 38.26 505.63 Tm (The )Tj 9.3212 0 0 9.3 58.33 505.63 Tm (property )Tj /T1_1 1 Tf 0 Tc 10.2 0 0 10.2 96.92 505.63 Tm [(F )138(F )119(N )]TJ /T1_3 1 Tf -0.035 Tc 8.2318 0 0 10 120.58 505.63 Tm (\(q )Tj /T1_2 1 Tf 0 Tc 10 0 0 10 130.95 505.63 Tm (-)Tj -0.035 Tc 8.362 0 0 10.5 140.13 505.63 Tm (1, )Tj /T1_3 1 Tf 8.3892 0 0 10 148.74 505.63 Tm (q\) )Tj /T1_0 1 Tf -0.0199 Tc 9.3 0 0 9.3 159.83 505.63 Tm (was )Tj 0.0234 Tc 1.899 0 Td (proved )Tj 0.0074 Tc 3.279 0 Td (for )Tj 0.0211 Tc 1.675 0 Td ("most" )Tj 0.05 Tc 9.5868 0 0 9.3 254.61 505.63 Tm (quadric )Tj 0.0218 Tc 9.3 0 0 9.3 289.97 505.63 Tm (hypersurfaces )Tj -0.006 Tc 6.205 0 Td (in )Tj /T1_2 1 Tf -0.035 Tc 7.8042 0 0 10.5 358.77 505.63 Tm ([1] )Tj /T1_0 1 Tf -0.0007 Tc 9.3 0 0 9.3 24.37 493.93 Tm (\(see )Tj -0.035 Tc 9.0221 0 0 10.9 43.88 493.93 Tm ([1, )Tj 0.0469 Tc 9.3 0 0 9.3 57.52 493.93 Tm (Theorem )Tj -0.035 Tc 9.5422 0 0 10.9 97.86 493.93 Tm (2.11] )Tj -0.0023 Tc 9.3 0 0 9.3 120.5 493.93 Tm (for )Tj 0 Tc 1.608 0 Td (a )Tj 0.0139 Tc 0.878 0 Td (more )Tj 0.0108 Tc 2.519 0 Td (precise )Tj 0.0366 Tc 3.346 0 Td (result\), )Tj 0.0074 Tc 3.494 0 Td (for )Tj 0.05 Tc 9.5723 0 0 9.3 245.84 493.93 Tm (Hermitian )Tj 0.0183 Tc 9.3 0 0 9.3 292.3 493.93 Tm (varieties )Tj 0.0327 Tc 3.923 0 Td (in )Tj -0.035 Tc 7.4675 0 0 10.9 340.74 493.93 Tm ([5] )Tj 0.0485 Tc 9.3 0 0 9.3 353.25 493.93 Tm (and )Tj -0.0023 Tc -35.44 -1.258 Td (for )Tj 0.05 Tc 9.3364 0 0 9.3 38.61 482.23 Tm (Grassmannians )Tj 9.3236 0 0 9.3 104.68 482.23 Tm (in )Tj -0.035 Tc 8.6539 0 0 10.7 116.25 482.23 Tm ([6, )Tj 0.034 Tc 9.3 0 0 9.3 128.8 482.23 Tm (Theorem )Tj -0.035 Tc 8.6913 0 0 10.7 167.89 482.23 Tm (2]. )Tj 0.0212 Tc 9.3 0 0 9.3 38.3 471.07 Tm (Here, )Tj -0.035 Tc 9.1156 0 0 9.3 63.35 471.07 Tm (we )Tj 0.0064 Tc 9.3 0 0 9.3 77.03 471.07 Tm (will )Tj 0.05 Tc 9.6893 0 0 9.3 94.54 471.07 Tm (study )Tj 9.4259 0 0 9.3 120.76 471.07 Tm (the )Tj -0.0016 Tc 9.3 0 0 9.3 136.78 471.07 Tm (Veronese )Tj 0.0355 Tc 4.114 0 Td (embeddings )Tj 0.039 Tc 5.478 0 Td (of )Tj 0 Tc 1.142 0 Td (a )Tj 0.05 Tc 9.337 0 0 9.3 244.45 471.07 Tm (projective )Tj 0.0276 Tc 9.3 0 0 9.3 289.13 471.07 Tm (space )Tj -0.0265 Tc 2.751 0 Td (\(see )Tj 0.034 Tc 1.881 0 Td (Theorem )Tj 0.0212 Tc 9.1 0 0 9.1 24.07 459.37 Tm (2.1\), )Tj 0.05 Tc 9.6991 0 0 9.3 45.52 459.37 Tm (the )Tj 0.0109 Tc 9.3 0 0 9.3 61.57 459.37 Tm (Segre )Tj 0.0304 Tc 2.668 0 Td (varieties )Tj -0.0136 Tc 4.016 0 Td (\(see )Tj 0.034 Tc 1.919 0 Td (Theorem )Tj -0.0005 Tc 9.1 0 0 9.1 180.49 459.37 Tm (2.2\) )Tj 0.05 Tc 9.5174 0 0 9.3 198.8 459.37 Tm (and )Tj 0.0396 Tc 9.3 0 0 9.3 216.88 459.37 Tm (the )Tj 0.0461 Tc 1.645 0 Td (minimal )Tj 0.0462 Tc 3.941 0 Td (degree )Tj 0.005 Tc 3.247 0 Td (scrolls )Tj -0.0136 Tc 3.002 0 Td (\(see )Tj 0.0173 Tc 1.9 0 Td (Theo\255)Tj 0.0462 Tc -34.483 -1.219 Td (rem )Tj 0.0158 Tc 2.086 0 Td (2.3\). )Tj 0.0302 Tc 2.478 0 Td (For )Tj 0.05 Tc 9.5625 0 0 9.3 83.14 448.03 Tm (the )Tj 0.0246 Tc 9.3 0 0 9.3 99.45 448.03 Tm (definitions )Tj 0.0272 Tc 4.972 0 Td (\(and )Tj 0.0268 Tc 2.255 0 Td (more )Tj 0.0361 Tc 2.498 0 Td (results\) )Tj -0.0119 Tc 3.63 0 Td (on )Tj 0.05 Tc 9.5625 0 0 9.3 236.68 448.03 Tm (the )Tj 0.0315 Tc 9.3 0 0 9.3 252.88 448.03 Tm (Veronese )Tj 0.0225 Tc 4.385 0 Td (embeddings, )Tj -0.0085 Tc 5.722 0 Td (Segre )Tj 0.0376 Tc -34.726 -1.239 Td (varieties )Tj 0.05 Tc 9.5174 0 0 9.3 61.46 436.51 Tm (and )Tj 0.0428 Tc 9.3 0 0 9.3 80.08 436.51 Tm (minimal )Tj 0.0113 Tc 3.941 0 Td (degree )Tj 0.0018 Tc 3.112 0 Td (scrolls, )Tj 0.05 Tc 9.4259 0 0 9.3 176.02 436.51 Tm (the )Tj 0.0469 Tc 9.3 0 0 9.3 192.23 436.51 Tm (reader )Tj -0.035 Tc 9.0754 0 0 9.3 221.15 436.51 Tm (is )Tj 0.0296 Tc 9.3 0 0 9.3 230.21 436.51 Tm (referred )Tj 0.05 Tc 9.8224 0 0 9.3 265.12 436.51 Tm (to )Tj 10.1089 0 0 9.3 277.36 436.51 Tm (the )Tj 0.0293 Tc 9.3 0 0 9.3 294.31 436.51 Tm (books )Tj /T1_2 1 Tf -0.035 Tc 7.8042 0 0 10.5 321.51 436.51 Tm ([4] )Tj /T1_0 1 Tf 0.0485 Tc 9.3 0 0 9.3 333.63 436.51 Tm (and )Tj /T1_2 1 Tf -0.035 Tc 8.593 0 0 10.5 351.91 436.51 Tm ([3]. )Tj /T1_0 1 Tf 0.05 Tc 10.0089 0 0 9.3 38.25 424.81 Tm (The )Tj 0.0463 Tc 9.3 0 0 9.3 59.5 424.81 Tm (last )Tj 0.0327 Tc 2.046 0 Td (section )Tj -0.0111 Tc 3.567 0 Td (is )Tj 0.0324 Tc 1.141 0 Td (devoted )Tj 0.0383 Tc 3.898 0 Td (to )Tj 0 Tc 1.347 0 Td (a )Tj 0.0335 Tc 0.949 0 Td (generalization )Tj 0.039 Tc 6.599 0 Td (of )Tj 0.05 Tc 9.5625 0 0 9.3 253.42 424.81 Tm (the )Tj 9.6593 0 0 9.3 271.27 424.81 Tm (property )Tj /T1_3 1 Tf 0 Tc 8.8 0 0 8.8 312.19 424.81 Tm [(F )50(F )]TJ /T1_1 1 Tf 0.05 Tc 9.9653 0 0 9.9 326.79 424.81 Tm (N\(k, )Tj /T1_3 1 Tf -0.035 Tc 8.3892 0 0 10 347.64 424.81 Tm (q\) )Tj /T1_0 1 Tf 0.0383 Tc 9.3 0 0 9.3 360.16 424.81 Tm (to )Tj 0.0238 Tc -36.162 -1.277 Td (curves. )Tj 0 Tc 13.8 0 0 13.8 24.58 381.25 Tm (2 )Tj 0.05 Tc 15.9483 0 0 13.8 48.1 381.25 Tm (The )Tj 15.3743 0 0 13.8 80.25 381.25 Tm (main )Tj 14.8572 0 0 13.8 119.14 381.25 Tm (results )Tj -0.0051 Tc 9.3 0 0 9.3 24.09 360.19 Tm (We )Tj 0.05 Tc 10.1703 0 0 9.3 40.36 360.19 Tm (start )Tj 0.0482 Tc 9.3 0 0 9.3 63.53 360.19 Tm (with )Tj 0.0348 Tc 2.325 0 Td (proving )Tj 0.05 Tc 9.5625 0 0 9.3 119.14 360.19 Tm (the )Tj -0.0067 Tc 9.3 0 0 9.3 135.26 360.19 Tm (following )Tj 0.0452 Tc 4.209 0 Td (theorem )Tj 0.0462 Tc 3.922 0 Td (on )Tj 0.0066 Tc 1.401 0 Td (Veronese )Tj 0.0379 Tc 4.219 0 Td (varieties. )Tj 0.05 Tc 10.8753 0 0 9.3 24.39 338.59 Tm (Theorem )Tj 9.3307 0 0 9.3 71.04 338.59 Tm (2.1 )Tj /T1_1 1 Tf -0.0047 Tc 9.9 0 0 9.9 89.9 338.59 Tm (Fix )Tj -0.0083 Tc 1.698 0 Td (positive )Tj -0.0183 Tc 3.445 0 Td (integers )Tj -0.035 Tc 8.859 0 0 9.9 175.27 338.59 Tm (d, )Tj /T1_0 1 Tf 0.042 Tc 9.3 0 0 9.3 186.64 338.59 Tm (m, )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 201.58 338.59 Tm (k )Tj -0.0183 Tc 0.941 0 Td (and )Tj -0.035 Tc 8.9958 0 0 9.9 228.55 338.59 Tm (q, )Tj -0.0196 Tc 9.9 0 0 9.9 240.25 338.59 Tm (with )Tj 0 Tc 2.054 0 Td [(q )-123(a )]TJ -0.0035 Tc 1.767 0 Td (power )Tj 0.0431 Tc 2.849 0 Td (of )Tj 0 Tc 1.129 0 Td (a )Tj -0.0158 Tc 0.785 0 Td (prime. )Tj -0.0197 Tc 3.14 0 Td (Let )Tj /T1_3 1 Tf 0 Tc 8.9 0 0 8.9 24.57 326.89 Tm (X )Tj /T1_2 1 Tf 10.9 0 0 10.9 36.24 326.89 Tm (c )Tj /T1_0 1 Tf 0.05 Tc 10.7383 0 0 9.8 46.28 326.89 Tm (pn, )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 65.11 326.89 Tm (n )Tj /T1_2 1 Tf 0.05 Tc 10.0859 0 0 8.4 73.71 326.89 Tm (:= )Tj /T1_1 1 Tf 0.0273 Tc 9.9 0 0 9.9 86.56 326.89 Tm (\(\(m )Tj /T1_2 1 Tf 0 Tc 12.7 0 0 12.7 104.01 326.89 Tm (+ )Tj /T1_1 1 Tf 0.0054 Tc 9.9 0 0 9.9 113.71 326.89 Tm (d\)!/\(m!d!\)\) )Tj /T1_0 1 Tf 0 Tc 4.757 0 Td (-)Tj -0.0205 Tc 9.3 0 0 9.3 169.78 326.89 Tm (1, )Tj /T1_1 1 Tf -0.035 Tc 8.3188 0 0 9.9 181.02 326.89 Tm (be )Tj -0.0251 Tc 9.9 0 0 9.9 192.48 326.89 Tm (the )Tj -0.0266 Tc 1.684 0 Td (Veronese )Tj -0.0055 Tc 3.956 0 Td (embedding )Tj 0.05 Tc 10.0385 0 0 9.9 294.94 326.89 Tm (of )Tj -0.035 Tc 9.1426 0 0 9.9 305.95 326.89 Tm (degree )Tj 0 Tc 9.9 0 0 9.9 332.77 326.89 Tm (d )Tj 0.0431 Tc 0.888 0 Td (of )Tj /T1_0 1 Tf 0.05 Tc 9.9012 0 0 9.8 351.56 326.89 Tm (pm. )Tj /T1_1 1 Tf 0.0042 Tc 9.9 0 0 9.9 25.72 315.19 Tm (Then )Tj /T1_3 1 Tf 0 Tc 8.9 0 0 8.9 49.59 315.19 Tm (X )Tj /T1_1 1 Tf 0.0006 Tc 9.9 0 0 9.9 61.77 315.19 Tm (satisfies )Tj 0.05 Tc 10.4859 0 0 9.9 97.28 315.19 Tm (FFN\(k,q\) )Tj 11.0386 0 0 9.9 145.12 315.19 Tm (if )Tj -0.0274 Tc 9.9 0 0 9.9 154.38 315.19 Tm (and )Tj -0.0212 Tc 1.816 0 Td (only )Tj 0.05 Tc 11.0386 0 0 9.9 192.1 315.19 Tm (if )Tj 0.0042 Tc 9.9 0 0 9.9 201.01 315.19 Tm (dk )Tj /C0_0 1 Tf 0 Tc 6.1201 0 0 7.3801 214.39 315.19 Tm <007E0020>Tj /T1_1 1 Tf -0.035 Tc 8.4817 0 0 9.9 224.05 315.19 Tm (q. )Tj /T1_0 1 Tf 0.0351 Tc 9.3 0 0 9.3 24.8 293.23 Tm (Proof. )Tj 0.0335 Tc 4.581 0 Td (Call )Tj /T1_3 1 Tf -0.035 Tc 6.0954 0 0 6.1 88.52 293.23 Tm (ZO, )Tj 0.05 Tc 8.8443 0 0 6.1 101.02 293.23 Tm (\225\225\225 )Tj 0 Tc 6.1 0 0 6.1 114.08 293.23 Tm (, )Tj 0.05 Tc 6.5076 0 0 6.1 117.86 293.23 Tm (Zm )Tj /T1_0 1 Tf 0.0492 Tc 9.3 0 0 9.3 132.64 293.23 Tm (the )Tj 0.0181 Tc 1.84 0 Td (homogeneous )Tj 0.0389 Tc 6.224 0 Td (coordinates )Tj 0.0133 Tc 5.498 0 Td (in )Tj 0.05 Tc 10.6799 0 0 9.6 270.74 293.23 Tm (pm, )Tj 9.3999 0 0 9.3 293.48 293.23 Tm (and )Tj /T1_1 1 Tf -0.035 Tc 9.5429 0 0 10.2 312.59 293.23 Tm (xo, )Tj 0 Tc 10.2 0 0 10.2 325.88 293.23 Tm (.)Tj /T1_0 1 Tf 0.05 Tc 10.2879 0 0 10.2 330.09 293.23 Tm (.. )Tj 0 Tc 10.2 0 0 10.2 338.42 293.23 Tm (, )Tj /T1_3 1 Tf 0.05 Tc 6.584 0 0 6.1 342.25 293.23 Tm (Xn )Tj /T1_0 1 Tf 0.0396 Tc 9.3 0 0 9.3 355.84 293.23 Tm (the )Tj 0.0297 Tc -35.592 -1.239 Td (homogeneous )Tj 0.0428 Tc 6.32 0 Td (coordinates )Tj 0.0133 Tc 5.478 0 Td (in )Tj 0.05 Tc 10.2014 0 0 9.8 146.18 281.71 Tm (pn, )Tj 0.0171 Tc 9.3 0 0 9.3 164.39 281.71 Tm (such )Tj 0.05 Tc 10.0691 0 0 9.3 186.46 281.71 Tm (that )Tj 0.0227 Tc 9.3 0 0 9.3 207.44 281.71 Tm (each )Tj /T1_1 1 Tf 0.05 Tc 7.9524 0 0 6.2 229.48 281.71 Tm (Xj )Tj /T1_0 1 Tf 0.0468 Tc 9.3 0 0 9.3 242.27 281.71 Tm (represents )Tj 0 Tc 4.985 0 Td (a )Tj 0.0092 Tc 0.929 0 Td (different )Tj 0.0075 Tc 3.987 0 Td (degree )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 363.73 281.71 Tm (d )Tj /T1_0 1 Tf 0.044 Tc 9.3 0 0 9.3 24.82 270 Tm (monomial )Tj 0.0327 Tc 4.716 0 Td (in )Tj 0.05 Tc 9.5625 0 0 9.3 79.9 270 Tm (the )Tj 0.0291 Tc 9.3 0 0 9.3 95.92 270 Tm (variables )Tj /T1_3 1 Tf -0.035 Tc 5.9826 0 0 6.1 135.14 270 Tm (ZO, )Tj 0.05 Tc 9.2627 0 0 6.1 147.62 270 Tm (.\225\225 )Tj 0 Tc 6.1 0 0 6.1 159.98 270 Tm (, )Tj 0.05 Tc 6.7229 0 0 6.1 163.58 270 Tm (Zm. )Tj /T1_0 1 Tf 9.6484 0 0 9.3 39.38 258.49 Tm (First )Tj 0.0372 Tc 9.3 0 0 9.3 61.47 258.49 Tm (assume )Tj /T1_1 1 Tf -0.014 Tc 9.9 0 0 9.9 93.37 258.49 Tm (dk )Tj /T1_2 1 Tf 0 Tc 11.1 0 0 11.1 106.56 258.49 Tm (< )Tj /T1_1 1 Tf 9.3 0 0 9.3 116.22 258.49 Tm (q )Tj /T1_0 1 Tf 0.05 Tc 9.3999 0 0 9.3 123.02 258.49 Tm (and )Tj 0.0414 Tc 9.3 0 0 9.3 140.14 258.49 Tm (let )Tj /T1_1 1 Tf -0.0152 Tc 10.2 0 0 10.2 153.08 258.49 Tm (F\(xo, )Tj 0.05 Tc 11.8554 0 0 10.2 177.19 258.49 Tm (... )Tj 0 Tc 10.2 0 0 10.2 189.94 258.49 Tm (, )Tj -0.0247 Tc 0.36 0 Td (xn\) )Tj /T1_0 1 Tf 0.05 Tc 9.7011 0 0 9.3 209.53 258.49 Tm (be )Tj 0 Tc 9.3 0 0 9.3 221.67 258.49 Tm (a )Tj 0.0394 Tc 0.705 0 Td (homogeneous )Tj 0.0265 Tc 6.273 0 Td (polynomial )Tj 0.039 Tc 5.041 0 Td (of )Tj 0.0075 Tc 1.026 0 Td (degree )Tj /T1_3 1 Tf 0 Tc -34.181 -1.219 Td (k )Tj /T1_0 1 Tf 0.05 Tc 9.3236 0 0 9.3 33.22 247.15 Tm (in )Tj /T1_1 1 Tf 0 Tc 10 0 0 10 44.41 247.15 Tm (n )Tj /T1_2 1 Tf 12.2 0 0 12.2 52.72 247.15 Tm (+ )Tj 9.3 0 0 9.3 62.16 247.15 Tm (1 )Tj /T1_0 1 Tf 0.0291 Tc 0.804 0 Td (variables )Tj 0.0151 Tc 4.212 0 Td (defined )Tj 0.0019 Tc 3.465 0 Td (over )Tj /T1_2 1 Tf 0 Tc 2.115 0 Td (F )Tj /T1_0 1 Tf -0.035 Tc 9.1941 0 0 10.3 167.31 247.15 Tm (q, )Tj 0.05 Tc 9.3999 0 0 9.3 177.74 247.15 Tm (and )Tj 0.0278 Tc 9.3 0 0 9.3 195.82 247.15 Tm (vanishing )Tj 0.0268 Tc 4.483 0 Td (on )Tj /T1_2 1 Tf 0 Tc 1.402 0 Td (X )Tj 0.05 Tc 9.3371 0 0 9.3 259.76 247.15 Tm (\(F )Tj /T1_0 1 Tf -0.035 Tc 9.5964 0 0 10.3 269.55 247.15 Tm (q\) )Tj 0 Tc 10.3 0 0 10.3 278.79 247.15 Tm (. )Tj 0.02 Tc 9.3 0 0 9.3 39.25 235.63 Tm (Since )Tj 0.05 Tc 9.5625 0 0 9.3 64.42 235.63 Tm (the )Tj 0.0339 Tc 9.3 0 0 9.3 80.98 235.63 Tm (variables )Tj /T1_3 1 Tf -0.035 Tc 7.6418 0 0 8.3 120.86 235.63 Tm (Xc, )Tj /T1_2 1 Tf 0.05 Tc 10.87 0 0 8.3 134.17 235.63 Tm (... )Tj /T1_3 1 Tf 8.8576 0 0 8.3 146.82 235.63 Tm (,X)Tj /T1_1 1 Tf 0 Tc 6.9001 0 0 6.9001 155.85 234.19 Tm (n )Tj /T1_0 1 Tf 0.0347 Tc 9.3 0 0 9.3 163.71 235.63 Tm (are )Tj 0 Tc 1.703 0 Td (a )Tj 0.0255 Tc 0.882 0 Td (basis )Tj 0.05 Tc 9.5989 0 0 9.3 211.23 235.63 Tm (of )Tj 0.0492 Tc 9.3 0 0 9.3 222.64 235.63 Tm (the )Tj 0.0322 Tc 1.761 0 Td (vector )Tj 0.05 Tc 9.5539 0 0 9.3 267.53 235.63 Tm (space )Tj 0.039 Tc 9.3 0 0 9.3 294.39 235.63 Tm (of )Tj 0.0103 Tc (all )Tj 0.0036 Tc 2.632 0 Td (degree )Tj /T1_1 1 Tf 0 Tc 9.6 0 0 9.6 347.71 235.63 Tm (d )Tj /T1_0 1 Tf -0.0162 Tc 9.3 0 0 9.3 356.03 235.63 Tm (ho\255)Tj 0.0267 Tc -35.595 -1.258 Td (mogeneous )Tj 0.0314 Tc 5.21 0 Td (polynomials )Tj 0.0327 Tc 5.623 0 Td (in )Tj /T1_2 1 Tf 0 Tc 8.6 0 0 8.6 136.63 223.93 Tm (m )Tj 12.7 0 0 12.7 147.03 223.93 Tm (+ )Tj 9.2 0 0 9.2 156.66 223.93 Tm (1 )Tj /T1_0 1 Tf 0.0217 Tc 9.3 0 0 9.3 163.96 223.93 Tm (variables, )Tj /T1_3 1 Tf 0 Tc 9.5 0 0 9.5 205.62 223.93 Tm (F )Tj /T1_0 1 Tf 0.0013 Tc 9.3 0 0 9.3 216.45 223.93 Tm (defines )Tj 0 Tc 3.31 0 Td (a )Tj 0.0355 Tc 0.86 0 Td (homogeneous )Tj 0.0244 Tc 6.312 0 Td (polynomial )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 361.48 223.93 Tm (G )Tj /T1_0 1 Tf 0.05 Tc 9.3902 0 0 9.3 24.75 212.23 Tm (of )Tj 0.0229 Tc 9.3 0 0 9.3 35.91 212.23 Tm (degree )Tj /T1_1 1 Tf -0.014 Tc 9.9 0 0 9.9 66.01 212.23 Tm (dk )Tj /T1_0 1 Tf 0.0303 Tc 9.3 0 0 9.3 79.54 212.23 Tm (vanishing )Tj 0.05 Tc 10.1984 0 0 9.3 121.4 212.23 Tm (at )Tj 0.0006 Tc 9.3 0 0 9.3 133.11 212.23 Tm (all )Tj 0.0319 Tc 1.404 0 Td (points )Tj 0.039 Tc 3.009 0 Td (of )Tj 0.05 Tc 9.9012 0 0 9.8 185.06 212.23 Tm (pm, )Tj 0.0151 Tc 9.3 0 0 9.3 205.29 212.23 Tm (defined )Tj 0.0083 Tc 3.503 0 Td (over )Tj /T1_2 1 Tf 0 Tc 9.5 0 0 9.5 258.43 212.23 Tm (F )Tj 0.05 Tc 8.012 0 0 6 265.24 212.23 Tm (q' )Tj /T1_0 1 Tf 0.0297 Tc 9.3 0 0 9.3 277.93 212.23 Tm (Since )Tj /T1_1 1 Tf -0.0322 Tc 9.9 0 0 9.9 303.25 212.23 Tm (dk )Tj /T1_0 1 Tf -0.035 Tc 5.8593 0 0 9.9 316.83 212.23 Tm (:::; )Tj /T1_1 1 Tf 8.7387 0 0 9.9 326.47 212.23 Tm (q, )Tj /T1_0 1 Tf 8.7957 0 0 9.3 336.95 212.23 Tm (we )Tj -0.0016 Tc 9.3 0 0 9.3 350.63 212.23 Tm (have )Tj 0 Tc 9.8 0 0 9.8 24.92 200.71 Tm (G )Tj 13 0 0 13 35.39 200.71 Tm (= )Tj 9.8 0 0 9.8 45.26 200.71 Tm (0 )Tj 0.0485 Tc 9.3 0 0 9.3 53.73 200.71 Tm (and )Tj 0.0187 Tc 1.944 0 Td (hence )Tj /T1_3 1 Tf 0.05 Tc 10.3558 0 0 9.3 97.96 200.71 Tm (FIX, )Tj /T1_0 1 Tf 9.4259 0 0 9.3 122.38 200.71 Tm (the )Tj 0.0325 Tc 9.3 0 0 9.3 138.41 200.71 Tm (restriction )Tj 0.0197 Tc 4.772 0 Td (of )Tj /T1_3 1 Tf 0 Tc 1.139 0 Td (F )Tj /T1_0 1 Tf 0.05 Tc 9.8224 0 0 9.3 203.92 200.71 Tm (to )Tj 9.9182 0 0 9.8 215.62 200.71 Tm (X, )Tj -0.0305 Tc 9.3 0 0 9.3 229.6 200.71 Tm (is )Tj -0.0009 Tc 1.048 0 Td (zero. )Tj -0.0088 Tc -21.494 -1.239 Td (Now, )Tj 0.0334 Tc 2.696 0 Td (assume )Tj /T1_1 1 Tf -0.014 Tc 9.9 0 0 9.9 97.87 189.19 Tm (dk )Tj /T1_2 1 Tf 0 Tc 11.2 0 0 11.2 112.32 189.19 Tm (> )Tj /T1_1 1 Tf -0.035 Tc 8.7387 0 0 9.9 122.89 189.19 Tm (q. )Tj /T1_0 1 Tf 0.0111 Tc 9.3 0 0 9.3 136 189.19 Tm (Take )Tj 0 Tc 2.496 0 Td (a )Tj 0.0239 Tc 0.88 0 Td (homogeneous )Tj 0.033 Tc 6.254 0 Td (polynomial )Tj /T1_2 1 Tf 0 Tc 9.4 0 0 9.4 274.89 189.19 Tm (G )Tj /T1_0 1 Tf 0.039 Tc 9.3 0 0 9.3 287.01 189.19 Tm (of )Tj 0.0113 Tc 1.219 0 Td (degree )Tj /T1_1 1 Tf -0.0322 Tc 9.9 0 0 9.9 327.91 189.19 Tm (dk )Tj /T1_0 1 Tf -0.0119 Tc 9.3 0 0 9.3 341.55 189.19 Tm (on )Tj 0.05 Tc 9.9697 0 0 9.8 354.98 189.19 Tm (pm )Tj 0.0351 Tc 9.3 0 0 9.3 25 177.67 Tm (vanishing )Tj 0.05 Tc 10.1984 0 0 9.3 67.58 177.67 Tm (at )Tj 0.0199 Tc 9.3 0 0 9.3 79.83 177.67 Tm (all )Tj 0.0474 Tc 1.462 0 Td (points )Tj 0.039 Tc 3.105 0 Td (of )Tj 0.05 Tc 10.2992 0 0 9.8 133.58 177.67 Tm (pm\(F )Tj -0.035 Tc 9.8724 0 0 10.3 157.77 177.67 Tm (q\), )Tj 0.05 Tc 9.7412 0 0 9.3 172.27 177.67 Tm (but )Tj 0.0482 Tc 9.3 0 0 9.3 189.89 177.67 Tm (with )Tj /T1_3 1 Tf 0 Tc 9.4 0 0 9.4 211.77 177.67 Tm (G )Tj /T1_1 1 Tf -0.035 Tc 3.2821 0 0 5.8001 223.11 177.67 Tm (=I=-)Tj /T1_0 1 Tf 7.2807 0 0 9.8 233.57 177.67 Tm (O. )Tj -0.0051 Tc 9.3 0 0 9.3 246.75 177.67 Tm (We )Tj 0.05 Tc 9.8153 0 0 9.3 263.68 177.67 Tm (may )Tj 0.04 Tc 9.3 0 0 9.3 285.82 177.67 Tm (take )Tj 0.0113 Tc 2.238 0 Td (as )Tj 0 Tc 9.8 0 0 9.8 318.68 177.67 Tm (G )Tj 9.3 0 0 9.3 329.31 177.67 Tm (a )Tj 0.0378 Tc 0.901 0 Td (product )Tj 0.039 Tc -33.63 -1.258 Td (of )Tj 0.0401 Tc 1.317 0 Td (linear )Tj 0.0062 Tc 2.979 0 Td (forms. )Tj 0.0357 Tc 3.605 0 Td (Every )Tj 0.0247 Tc 3.061 0 Td (monomial )Tj 0.039 Tc 4.715 0 Td (of )Tj 0.0191 Tc 1.277 0 Td (degree )Tj /T1_1 1 Tf -0.014 Tc 9.9 0 0 9.9 213.25 165.97 Tm (dk )Tj /T1_0 1 Tf 0.0133 Tc 9.3 0 0 9.3 227.62 165.97 Tm (in )Tj 0.05 Tc 9.4259 0 0 9.3 239.92 165.97 Tm (the )Tj 0.0436 Tc 9.3 0 0 9.3 257.38 165.97 Tm (variables )Tj /T1_3 1 Tf -0.035 Tc 6.0954 0 0 6.1 298.94 165.97 Tm (ZO, )Tj 0.05 Tc 8.5227 0 0 6.1 311.45 165.97 Tm (\225\225\225 )Tj 6.3871 0 0 6.1 323.6 165.97 Tm (Zm )Tj /T1_0 1 Tf 0.0229 Tc 9.3 0 0 9.3 338.38 165.97 Tm (may )Tj 0.015 Tc 2.268 0 Td (be )Tj 0.0409 Tc -35.963 -1.219 Td (represented )Tj 0.05 Tc 9.3045 0 0 9.3 76.03 154.63 Tm (\(not )Tj 0.0246 Tc 9.3 0 0 9.3 96.12 154.63 Tm (uniquely\) )Tj 0.0161 Tc 4.472 0 Td (by )Tj 0 Tc 1.402 0 Td (a )Tj 0.0302 Tc 0.82 0 Td (monomial )Tj 0.05 Tc 9.3902 0 0 9.3 201.33 154.63 Tm (of )Tj 0.0152 Tc 9.3 0 0 9.3 212.13 154.63 Tm (degree )Tj /T1_3 1 Tf 0 Tc 3.174 0 Td (k )Tj /T1_0 1 Tf 0.05 Tc 9.3236 0 0 9.3 249.58 154.63 Tm (in )Tj 9.5625 0 0 9.3 260.8 154.63 Tm (the )Tj 0.0315 Tc 9.3 0 0 9.3 277.54 154.63 Tm (variables )Tj /T1_3 1 Tf -0.035 Tc 7.5144 0 0 8.3 316.88 154.63 Tm (Xc, )Tj /T1_2 1 Tf 0.05 Tc 11.0751 0 0 8.3 330 154.63 Tm (... )Tj /T1_3 1 Tf 0.0491 Tc 8.3 0 0 8.3 342.85 154.63 Tm (,X)Tj /T1_1 1 Tf 0 Tc 6.9001 0 0 6.9001 351.33 153 Tm (n)Tj 0.752 0.236 Td (. )Tj /T1_0 1 Tf 0.0111 Tc 9.3 0 0 9.3 39.56 143.11 Tm (Hence, )Tj -0.035 Tc 9.1156 0 0 9.3 74.87 143.11 Tm (we )Tj 0.0422 Tc 9.3 0 0 9.3 92.68 143.11 Tm (may )Tj 0.0275 Tc 2.605 0 Td (associate )Tj 0.05 Tc 9.3858 0 0 9.3 159.64 143.11 Tm (to )Tj /T1_2 1 Tf 0 Tc 9.2 0 0 9.2 174.64 143.11 Tm (G )Tj /T1_0 1 Tf 9.3 0 0 9.3 188.73 143.11 Tm (a )Tj 0.0239 Tc 1.247 0 Td (homogeneous )Tj 0.048 Tc 6.602 0 Td (polynomial )Tj 0.0197 Tc 5.718 0 Td (of )Tj 0.0075 Tc 1.51 0 Td (degree )Tj /T1_3 1 Tf -0.035 Tc 8.6597 0 0 9.3 361.36 143.11 Tm (k, )Tj /T1_1 1 Tf -0.002 Tc 10.2 0 0 10.2 25.46 131.41 Tm (F\(xo, )Tj /T1_0 1 Tf 0.05 Tc 11.8158 0 0 10.2 50.33 131.41 Tm (... )Tj /T1_1 1 Tf 11.9005 0 0 10.2 63.22 131.41 Tm (,x)Tj 0 Tc 6.9001 0 0 6.9001 72.33 129.79 Tm (n)Tj 0.05 Tc 7.535 0 0 6.9001 77.47 131.41 Tm (\), )Tj /T1_0 1 Tf 0.0158 Tc 9.3 0 0 9.3 86.75 131.41 Tm (whose )Tj 0.0345 Tc 3.077 0 Td (restriction )Tj 0.0383 Tc 4.818 0 Td (to )Tj /T1_1 1 Tf 0 Tc 10.2 0 0 10.2 172.11 131.41 Tm (X )Tj /T1_0 1 Tf 0.0263 Tc 9.3 0 0 9.3 184.06 131.41 Tm (induces )Tj -0.035 Tc 9.3715 0 0 10.3 218.25 131.41 Tm (G, )Tj 0.05 Tc 9.5174 0 0 9.3 231.38 131.41 Tm (and )Tj 0.0187 Tc 9.3 0 0 9.3 250.37 131.41 Tm (hence )Tj 0.029 Tc 2.902 0 Td (vanishes )Tj 0.05 Tc 9.7241 0 0 9.3 315.26 131.41 Tm (at )Tj 0.0163 Tc 9.3 0 0 9.3 326.78 131.41 Tm (each )Tj 0.0307 Tc 2.296 0 Td (point )Tj 0.05 Tc 9.3902 0 0 9.3 24.93 119.53 Tm (of )Tj /T1_3 1 Tf 10.9073 0 0 9.3 36.11 119.53 Tm (X\(F )Tj /T1_0 1 Tf -0.035 Tc 9.5134 0 0 10.3 55.53 119.53 Tm (q\). )Tj 0.02 Tc 9.3 0 0 9.3 39.43 108.01 Tm (Since )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 64.7 108.01 Tm (F )Tj /T1_0 1 Tf 0.0327 Tc 9.3 0 0 9.3 74.8 108.01 Tm (induces )Tj /T1_3 1 Tf -0.0342 Tc 3.618 0 Td (G, )Tj /T1_0 1 Tf -0.035 Tc 8.9557 0 0 9.3 121.85 108.01 Tm (we )Tj 0.0113 Tc 9.3 0 0 9.3 135.53 108.01 Tm (have )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 157.22 108.01 Tm (F )Tj -0.035 Tc 6.9854 0 0 11.6 166.84 108.01 Tm (=I )Tj /T1_0 1 Tf 9.0857 0 0 9.3 176.67 108.01 Tm (0, )Tj 0.05 Tc 10.0691 0 0 9.3 187 108.01 Tm (that )Tj -0.0111 Tc 9.3 0 0 9.3 207.46 108.01 Tm (is )Tj /T1_1 1 Tf 0 Tc 9.9 0 0 9.9 217.52 108.01 Tm [(F )134(F )]TJ 0.05 Tc 10.157 0 0 9.9 231.75 108.01 Tm (N\(k, )Tj -0.035 Tc 8.9618 0 0 9.9 253.39 108.01 Tm (q\) )Tj /T1_0 1 Tf -0.0305 Tc 9.3 0 0 9.3 264.7 108.01 Tm (is )Tj 0.0272 Tc 1.004 0 Td (false )Tj -0.0023 Tc 2.381 0 Td (for )Tj /T1_3 1 Tf 0.05 Tc 9.7553 0 0 9.3 310.78 108.01 Tm (X. )Tj /T1_0 1 Tf 0 Tc 8.4 0 0 8.4 362.43 108.01 Tm (0 )Tj 0.0326 Tc 9.3 0 0 9.3 39.64 96.49 Tm (Next, )Tj -0.035 Tc 8.9557 0 0 9.3 65.33 96.49 Tm (we )Tj 0.0308 Tc 9.3 0 0 9.3 79.29 96.49 Tm (consider )Tj /T1_3 1 Tf 0 Tc 8.9 0 0 8.9 116.34 96.49 Tm [(F )60(F )]TJ /T1_1 1 Tf 0.05 Tc 9.9653 0 0 9.9 131.31 96.49 Tm (N\(k, )Tj -0.035 Tc 8.732 0 0 9.9 152.41 96.49 Tm (q\) )Tj /T1_0 1 Tf -0.012 Tc 9.3 0 0 9.3 163.16 96.49 Tm (for )Tj 0.0109 Tc 1.541 0 Td (Segre )Tj 0.0207 Tc 2.687 0 Td (varieties. )Tj 0.05 Tc 10.8291 0 0 9.3 25.29 74.71 Tm (Theorem )Tj 9.6011 0 0 9.3 71.76 74.71 Tm (2.2 )Tj /T1_1 1 Tf -0.0047 Tc 9.9 0 0 9.9 90.62 74.71 Tm (Fix )Tj -0.0057 Tc 1.698 0 Td (positive )Tj -0.0183 Tc 3.482 0 Td (integers )Tj -0.035 Tc 8.9958 0 0 9.9 176.17 74.71 Tm (q, )Tj -0.0014 Tc 9.9 0 0 9.9 187.14 74.71 Tm (r, )Tj 0.05 Tc 11.4152 0 0 9.9 198.58 74.71 Tm (sand )Tj /T1_0 1 Tf 0.042 Tc 9.3 0 0 9.3 224.98 74.71 Tm (m, )Tj /T1_1 1 Tf -0.0196 Tc 9.9 0 0 9.9 240.43 74.71 Tm (with )Tj 0 Tc 2.035 0 Td [(q )-159(a )]TJ -0.0081 Tc 1.767 0 Td (power )Tj 0.0431 Tc 2.85 0 Td (of )Tj 0 Tc 1.129 0 Td (a )Tj -0.0121 Tc 0.785 0 Td (prime, )Tj -0.035 Tc 9.8792 0 0 9.9 355.26 74.71 Tm (and )Tj 0.0116 Tc 9.9 0 0 9.9 25.59 63.37 Tm (set )Tj /T1_2 1 Tf 0 Tc 8.2 0 0 8.2 39.98 63.37 Tm (m )Tj 0.05 Tc 9.8758 0 0 8.4 51.94 63.37 Tm (:= )Tj /T1_1 1 Tf 10.2328 0 0 9.9 64.38 63.37 Tm (rs )Tj /T1_2 1 Tf 0 Tc 12.7 0 0 12.7 75.39 63.37 Tm (+ )Tj /T1_1 1 Tf 9.9 0 0 9.9 85.08 63.37 Tm (r )Tj /T1_2 1 Tf 12.7 0 0 12.7 91.95 63.37 Tm (+ )Tj /T1_1 1 Tf -0.0341 Tc 9.9 0 0 9.9 101.91 63.37 Tm (s. )Tj -0.0015 Tc 1.225 0 Td (Let )Tj 0 Tc 1.628 0 Td (X )Tj /T1_2 1 Tf 0.05 Tc 10.296 0 0 8.1 141.21 63.37 Tm (:= )Tj /T1_0 1 Tf 10.1063 0 0 9.6 153.92 63.37 Tm (pm )Tj 0 Tc 7.1 0 0 7.1 171.17 63.37 Tm (X )Tj 0.05 Tc 10.6453 0 0 9.6 179.48 63.37 Tm (ps )Tj 0 Tc 8.3 0 0 8.3 193.42 63.37 Tm (C )Tj 0.05 Tc 11.2393 0 0 9.6 203.6 63.37 Tm (pn )Tj /T1_1 1 Tf -0.035 Tc 7.913 0 0 9.9 220.08 63.37 Tm (be )Tj -0.0069 Tc 9.9 0 0 9.9 231 63.37 Tm (the )Tj -0.035 Tc 9.732 0 0 9.9 246.95 63.37 Tm (Segre )Tj 0.021 Tc 9.9 0 0 9.9 271.74 63.37 Tm (variety )Tj -0.0321 Tc 3.31 0 Td (defined )Tj -0.0274 Tc 3.142 0 Td (over )Tj /T1_0 1 Tf 0 Tc 9.6 0 0 9.6 355.46 63.37 Tm (F)Tj 6.2 0 0 6.2 361.74 61.75 Tm (q)Tj 0.831 0.261 Td (. )Tj /T1_1 1 Tf 0.0042 Tc 9.9 0 0 9.9 26.44 51.67 Tm (Then )Tj 0 Tc 2.422 0 Td (X )Tj -0.0016 Tc 1.219 0 Td (satisfies )Tj 0 Tc 3.569 0 Td [(F )97(F )]TJ 0.05 Tc 10.2808 0 0 9.9 112.95 51.67 Tm (N\( )Tj -0.035 Tc 8.9958 0 0 9.9 124.69 51.67 Tm (q, )Tj 9.7363 0 0 9.9 133.5 51.67 Tm (q\). )Tj /T1_0 1 Tf -0.0174 Tc 9.3 0 0 9.3 192.83 18.91 Tm (58 )Tj ET endstream endobj 60 0 obj <>/Filter/CCITTFaxDecode/Height 1872/Length 56400/Name/Im0/Subtype/Image/Type/XObject/Width 2240>>stream +Q)Q#JQDrJ2*9RGQR.2*2j2J2CRRRA (A rH (JrH (JrH9MABJrJ%dJdK 2J9RGQR.9RRF@TG *T:#X#pG3! 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)Tj 0.0158 Tc 2.66 0 Td (varieties, )Tj 0.038 Tc 4.275 0 Td (the )Tj 0.0054 Tc 1.762 0 Td (minimal )Tj -0.0019 Tc 3.799 0 Td (degree )Tj 0.0304 Tc 3.121 0 Td (rational )Tj 0.0133 Tc 3.699 0 Td (scrolls )Tj 0.05 Tc 9.7524 0 0 9.6 310.22 255.61 Tm (and )Tj 0.0474 Tc 9.6 0 0 9.6 329.74 255.61 Tm (the )Tj 0.0165 Tc -29.687 -1.237 Td (linearly )Tj 0.0422 Tc 3.514 0 Td (normal )Tj 0.0198 Tc 3.384 0 Td (embeddings )Tj -0.0064 Tc 5.382 0 Td (of )Tj 0.0277 Tc 1.082 0 Td (smooth )Tj -0.0105 Tc 3.399 0 Td (curves. )Tj 0 Tc 13.7 0 0 13.7 22.2 211.87 Tm (1 )Tj 0.05 Tc 15.7143 0 0 13.7 44.53 211.87 Tm (Introduction )Tj -0.017 Tc 9.6 0 0 9.6 22.1 190.81 Tm (Following )Tj -0.035 Tc 8.7489 0 0 11.1 63.69 190.81 Tm ([1], )Tj 8.89 0 0 11.1 79.53 190.81 Tm ([5], )Tj 8.6078 0 0 11.1 96.09 190.81 Tm ([6], )Tj 9.1156 0 0 9.6 111.05 190.81 Tm (we )Tj -0.0122 Tc 9.6 0 0 9.6 124.84 190.81 Tm (give )Tj 0.05 Tc 9.6991 0 0 9.6 144.52 190.81 Tm (the )Tj -0.0171 Tc 9.6 0 0 9.6 160.63 190.81 Tm (following )Tj 0.0019 Tc 4.108 0 Td (definition. )Tj 0.05 Tc 10.0718 0 0 9.6 21.91 169.03 Tm (Definition )Tj 9.573 0 0 9.3 71.85 169.03 Tm (1.1 )Tj /T1_2 1 Tf 0.0226 Tc 9.9 0 0 9.9 90.8 169.03 Tm (Fix )Tj -0.0031 Tc 1.625 0 Td (positive )Tj -0.0079 Tc 3.355 0 Td (integers )Tj 0 Tc 3.446 0 Td (k )Tj -0.0092 Tc 0.796 0 Td (and )Tj -0.035 Tc 8.7387 0 0 9.9 198.85 169.03 Tm (q, )Tj -0.0196 Tc 9.9 0 0 9.9 208.93 169.03 Tm (with )Tj 0 Tc 1.908 0 Td [(q )-14(a )]TJ -0.0126 Tc 1.458 0 Td (power )Tj 0.05 Tc 10.0385 0 0 9.9 269.02 169.03 Tm (of )Tj 0 Tc 9.9 0 0 9.9 278.94 169.03 Tm (a )Tj 0.0133 Tc 0.73 0 Td (prime. )Tj -0.0015 Tc 3.213 0 Td (Let )Tj /T1_0 1 Tf 0 Tc 9.6 0 0 9.6 332.8 169.03 Tm (X )Tj 9.3 0 0 9.3 344.6 169.03 Tm (C )Tj /T1_1 1 Tf 0.05 Tc 9.8748 0 0 9.1 354.05 169.03 Tm (pn )Tj /T1_2 1 Tf -0.035 Tc 8.3188 0 0 9.9 22.44 157.33 Tm (be )Tj 9.4125 0 0 9.9 33.96 157.33 Tm (an )Tj -0.0185 Tc 9.9 0 0 9.9 46.5 157.33 Tm (irreducible )Tj -0.0039 Tc 4.645 0 Td (projective )Tj 0.0058 Tc 4.324 0 Td (variety )Tj 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)Tj /T1_0 1 Tf -0.035 Tc 9.8249 0 0 10.3 58.41 133.93 Tm (q\) )Tj /T1_2 1 Tf 0.05 Tc 11.0386 0 0 9.9 71.14 133.93 Tm (if )Tj 0.004 Tc 9.9 0 0 9.9 81.27 133.93 Tm (every )Tj -0.0117 Tc 2.604 0 Td (homogeneous )Tj -0.0135 Tc 5.784 0 Td (polynomial )Tj -0.0153 Tc 4.795 0 Td (over )Tj /T1_1 1 Tf 0 Tc 9.3 0 0 9.3 232.16 133.93 Tm (F )Tj /T1_0 1 Tf 10.3 0 0 10.3 238.94 133.93 Tm (q )Tj /T1_2 1 Tf 0.05 Tc 10.2615 0 0 9.9 248.31 133.93 Tm (of )Tj -0.035 Tc 9.1426 0 0 9.9 260.23 133.93 Tm (degree )Tj 0 Tc 9.9 0 0 9.9 288.34 133.93 Tm (k )Tj -0.0163 Tc 0.994 0 Td (on )Tj /T1_1 1 Tf 0.05 Tc 10.3526 0 0 9.1 311.56 133.93 Tm (pn )Tj /T1_2 1 Tf -0.0099 Tc 9.9 0 0 9.9 328.8 133.93 Tm (vanishing )Tj -0.035 Tc 9.7154 0 0 9.9 22.6 122.22 Tm (on )Tj 0 Tc 9.9 0 0 9.9 36.38 122.22 Tm (X )Tj /T1_0 1 Tf 0.0212 Tc 10.3 0 0 10.3 44.52 122.22 Tm (\(F )Tj -0.035 Tc 8.9109 0 0 10.3 54.28 122.22 Tm (q\) )Tj /T1_2 1 Tf 0.0081 Tc 9.9 0 0 9.9 67.08 122.22 Tm (vanishes )Tj -0.035 Tc 9.7154 0 0 9.9 106.48 122.22 Tm (on )Tj /T1_0 1 Tf 0.05 Tc 10.6266 0 0 10.3 119.86 122.22 Tm (X, )Tj /T1_2 1 Tf -0.0077 Tc 9.9 0 0 9.9 136.57 122.22 Tm (namely, )Tj 0.0084 Tc 3.666 0 Td (it )Tj -0.0127 Tc 1.006 0 Td (vanishes )Tj -0.0227 Tc 3.8 0 Td (at )Tj -0.0317 Tc 1.218 0 Td (all )Tj 0.0009 Tc 1.403 0 Td (points )Tj 0.05 Tc 10.2615 0 0 9.9 274.95 122.22 Tm (of )Tj /T1_0 1 Tf 0 Tc 10.3 0 0 10.3 286.72 122.22 Tm (X )Tj /T1_2 1 Tf -0.014 Tc 9.9 0 0 9.9 300.55 122.22 Tm (defined )Tj 0.009 Tc 3.27 0 Td (over )Tj -0.0342 Tc 2.214 0 Td (the )Tj -0.035 Tc 9.6606 0 0 9.9 22.62 110.53 Tm (algebraic )Tj -0.0243 Tc 9.9 0 0 9.9 60.94 110.53 Tm (closure )Tj 0.05 Tc 10.4846 0 0 9.9 93.15 110.53 Tm (of )Tj /T1_0 1 Tf 0 Tc 10 0 0 10 103.82 110.53 Tm (F )Tj /T1_1 1 Tf 0.05 Tc 8.2477 0 0 5.7 110.26 110.53 Tm (q' )Tj /T1_0 1 Tf -0.035 Tc 8.8371 0 0 9.6 35.97 88.93 Tm (We )Tj 0.0186 Tc 9.6 0 0 9.6 51.88 88.93 Tm (stress )Tj 0.05 Tc 10.6163 0 0 9.6 78.45 88.93 Tm (that )Tj 0.038 Tc 9.6 0 0 9.6 100.06 88.93 Tm (the )Tj 0.05 Tc 10.1888 0 0 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