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(dim\(V\(K\) )Tj
/T1_0 1 Tf
0 Tc 12.5 0 0 12.5 258.64 433.63 Tm
(n )Tj
/T1_1 1 Tf
0.05 Tc 10.3797 0 0 9.8 268.29 433.63 Tm
(Hi\(K\)\) )Tj
/T1_2 1 Tf
0 Tc 8.1 0 0 8.1 304.97 433.63 Tm
(= )Tj
/T1_1 1 Tf
0.0108 Tc 9.6 0 0 9.6 316.91 433.63 Tm
(x, )Tj
/T1_0 1 Tf
-0.0086 Tc 9.4 0 0 9.4 328.76 433.63 Tm
(for )Tj
0.0007 Tc 1.666 0 Td
(every )Tj
0 Tc -34.761 -1.226 Td
(1 )Tj
/C0_0 1 Tf
5.9401 0 0 7.3801 25.39 422.11 Tm
<007E0020>Tj
/T1_2 1 Tf
8.6 0 0 8.6 35.47 422.11 Tm
(i )Tj
/C0_0 1 Tf
5.9401 0 0 7.3801 42.31 422.11 Tm
<007E0020>Tj
/T1_1 1 Tf
-0.0093 Tc 9.1 0 0 9.1 52.5 422.11 Tm
(a, )Tj
/T1_0 1 Tf
0.05 Tc 10.1049 0 0 9.4 63.62 422.11 Tm
(and )Tj
10.2879 0 0 9.4 83.31 422.11 Tm
(that )Tj
/T1_1 1 Tf
10.4289 0 0 9.8 104.37 422.11 Tm
(V\(K\) )Tj
/T1_0 1 Tf
0 Tc 12.5 0 0 12.5 130.48 422.11 Tm
(n )Tj
/T1_1 1 Tf
0.047 Tc 9.8 0 0 9.8 139.4 422.11 Tm
(Hi\(K\) )Tj
-0.035 Tc 8.4777 0 0 9.4 168.95 422.11 Tm
(of )Tj
0.05 Tc 10.4289 0 0 9.8 179.07 422.11 Tm
(V\(K\) )Tj
/T1_0 1 Tf
0 Tc 12.5 0 0 12.5 205 422.11 Tm
(n )Tj
/T1_1 1 Tf
-0.0086 Tc 9.8 0 0 9.8 213.74 422.11 Tm
(Hj\(I<\) )Tj
/T1_0 1 Tf
0 Tc 2.842 0 Td
(, )Tj
-0.0181 Tc 9.4 0 0 9.4 246.68 422.11 Tm
(for )Tj
/T1_2 1 Tf
0 Tc 8.6 0 0 8.6 261.55 422.11 Tm
(i )Tj
/T1_1 1 Tf
-0.035 Tc 5.5807 0 0 10 268.04 422.11 Tm
(=I-)Tj
/T1_0 1 Tf
0.05 Tc 11.2648 0 0 8.8 279.08 422.11 Tm
(j. )Tj
9.7067 0 0 9.4 291.52 422.11 Tm
(Thus )Tj
0 Tc 9.4 0 0 9.4 316.58 422.11 Tm
(D )Tj
0.0253 Tc 1.164 0 Td
(intersects )Tj
0.0097 Tc -32.977 -1.206 Td
(each )Tj
/T1_1 1 Tf
-0.035 Tc 7.9143 0 0 9.4 39.5 410.77 Tm
(Ll!i\(G\(:z; )Tj
/T1_0 1 Tf
0 Tc 9.4 0 0 9.4 71.53 410.77 Tm
(-)Tj
-0.035 Tc 9.2294 0 0 9.4 81.94 410.77 Tm
(1, )Tj
/T1_1 1 Tf
0.05 Tc 10.2134 0 0 9.6 90.85 410.77 Tm
(n\)\(K\)\) )Tj
/T1_0 1 Tf
9.9612 0 0 9.4 123.56 410.77 Tm
(at )Tj
0 Tc 9.4 0 0 9.4 135.62 410.77 Tm
(a )Tj
0.0117 Tc 0.882 0 Td
(different )Tj
0.0236 Tc 3.994 0 Td
(point. )Tj
0.0044 Tc 3.102 0 Td
(Since )Tj
0.05 Tc 9.4634 0 0 9.4 235.71 410.77 Tm
(deg\(J\) )Tj
/T1_2 1 Tf
0 Tc 8.1 0 0 8.1 266.45 410.77 Tm
(= )Tj
/T1_3 1 Tf
8.3 0 0 8.3 277.61 410.77 Tm
(t )Tj
/C0_0 1 Tf
5.9401 0 0 7.3801 285.31 410.77 Tm
<007E0020>Tj
/T1_1 1 Tf
8.7 0 0 8.7 296.05 410.77 Tm
(q )Tj
/T1_2 1 Tf
10.8 0 0 10.8 304.75 410.77 Tm
(< )Tj
/T1_1 1 Tf
-0.035 Tc 8.9213 0 0 9.6 315.12 410.77 Tm
(a, )Tj
/T1_0 1 Tf
8.7957 0 0 9.4 325.97 410.77 Tm
(we )Tj
0.0408 Tc 9.4 0 0 9.4 340.11 410.77 Tm
(obtain )Tj
/T1_3 1 Tf
0.05 Tc 11.3603 0 0 10 17.67 399.25 Tm
(flD )Tj
/C0_0 1 Tf
0 Tc 6.3001 0 0 7.3801 37.27 399.25 Tm
<007E0020>Tj
/T1_0 1 Tf
-0.035 Tc 6.8872 0 0 9.6 47.27 399.25 Tm
(O. )Tj
0.0284 Tc 9.4 0 0 9.4 59.77 399.25 Tm
(Since )Tj
0.05 Tc 12.36 0 0 9.6 85.55 399.25 Tm
(QED, )Tj
-0.035 Tc 8.7957 0 0 9.4 119.87 399.25 Tm
(we )Tj
0.0485 Tc 9.4 0 0 9.4 133.83 399.25 Tm
(obtain )Tj
/T1_3 1 Tf
0.05 Tc 10.0644 0 0 10 163.49 399.25 Tm
(f\(Q\) )Tj
/T1_0 1 Tf
0 Tc 12.1 0 0 12.1 186.96 399.25 Tm
(= )Tj
-0.035 Tc 8.8261 0 0 9.4 197.01 399.25 Tm
(0, )Tj
9.39 0 0 9.4 207.8 399.25 Tm
(as )Tj
0.0208 Tc 9.4 0 0 9.4 219.41 399.25 Tm
(wanted. )Tj
0.0027 Tc 3.912 0 Td
(Now, )Tj
-0.035 Tc 9.1156 0 0 9.4 281.51 399.25 Tm
(we )Tj
0.0226 Tc 9.4 0 0 9.4 296.01 399.25 Tm
(consider )Tj
0.05 Tc 9.5625 0 0 9.4 332.98 399.25 Tm
(the )Tj
-0.0043 Tc 9.4 0 0 9.4 349.47 399.25 Tm
(case )Tj
/T1_1 1 Tf
0 Tc 9.6 0 0 9.6 17.93 387.73 Tm
(x )Tj
/T1_0 1 Tf
11.3 0 0 11.3 25.5 387.73 Tm
(= )Tj
/T1_1 1 Tf
9.6 0 0 9.6 35.95 387.73 Tm
(n )Tj
/T1_0 1 Tf
0.837 0 Td
(-)Tj
-0.0259 Tc 9.1 0 0 9.1 53.33 387.73 Tm
(1. )Tj
0.05 Tc 9.5709 0 0 9.4 64.77 387.73 Tm
(We )Tj
0.0237 Tc 9.4 0 0 9.4 82.25 387.73 Tm
(have )Tj
/T1_1 1 Tf
0.05 Tc 9.9081 0 0 9.6 104.2 387.73 Tm
(G\(n )Tj
/T1_0 1 Tf
0 Tc 9.6 0 0 9.6 123.73 387.73 Tm
(-)Tj
-0.035 Tc 8.9497 0 0 9.4 133.43 387.73 Tm
(1, )Tj
/T1_1 1 Tf
0.0458 Tc 9.6 0 0 9.6 142.15 387.73 Tm
(n\) )Tj
/T1_2 1 Tf
0 Tc 8.1 0 0 8.1 154.31 387.73 Tm
(= )Tj
/T1_0 1 Tf
-0.035 Tc 7.1287 0 0 9.4 163.92 387.73 Tm
(lP)Tj
/T1_2 1 Tf
0 Tc 5.3001 0 0 5.3001 169.46 391.33 Tm
(n)Tj
9.1 0 0 9.1 174.52 387.73 Tm
(* )Tj
/C0_0 1 Tf
6.3001 0 0 7.2001 181.09 387.73 Tm
<007E0020>Tj
/T1_0 1 Tf
0.05 Tc 9.7036 0 0 9.4 190.91 387.73 Tm
(IF, )Tj
9.4 0 0 9.4 207.08 387.73 Tm
(and )Tj
9.5625 0 0 9.4 225.52 387.73 Tm
(the )Tj
0.0352 Tc 9.4 0 0 9.4 242.11 387.73 Tm
(proof )Tj
-0.0179 Tc 2.595 0 Td
(is )Tj
0.0408 Tc 1.089 0 Td
(as )Tj
0.0202 Tc 1.264 0 Td
(for )Tj
0.05 Tc 9.5625 0 0 9.4 304 387.73 Tm
(the )Tj
-0.0107 Tc 9.4 0 0 9.4 320.31 387.73 Tm
(case )Tj
/T1_1 1 Tf
0 Tc 9.6 0 0 9.6 340.13 387.73 Tm
(x )Tj
/T1_0 1 Tf
11.4 0 0 11.4 348.06 387.73 Tm
(= )Tj
-0.035 Tc 6.4936 0 0 9.6 357.96 387.73 Tm
(O. )Tj
0.05 Tc 10.4108 0 0 9.4 17.8 366.67 Tm
(Acknowledgement. )Tj
0.0454 Tc 9.4 0 0 9.4 117.28 366.67 Tm
(This )Tj
0.0172 Tc 2.784 0 Td
(research )Tj
-0.0184 Tc 4.328 0 Td
(was )Tj
0.0296 Tc 2.385 0 Td
(carried )Tj
0.05 Tc 9.4206 0 0 9.4 242.55 366.67 Tm
(out )Tj
9.5836 0 0 9.4 263.87 366.67 Tm
(within )Tj
9.6991 0 0 9.4 299.5 366.67 Tm
(the )Tj
0.0334 Tc 9.4 0 0 9.4 320.48 366.67 Tm
(activity )Tj
0.0108 Tc 4.061 0 Td
(of )Tj
0.0329 Tc -36.23 -1.226 Td
(G.N.S.A.G.A. )Tj
0.0491 Tc 6.664 0 Td
(of )Tj
0.05 Tc 9.5625 0 0 9.4 93.22 355.15 Tm
(the )Tj
0.0498 Tc 9.4 0 0 9.4 110.99 355.15 Tm
(Italian )Tj
0.0218 Tc 3.386 0 Td
(C.N.R. )Tj
0.035 Tc 3.514 0 Td
(with )Tj
0.05 Tc 9.5625 0 0 9.4 198.52 355.15 Tm
(the )Tj
9.5121 0 0 9.4 215.87 355.15 Tm
(support )Tj
0.03 Tc 9.4 0 0 9.4 252.45 355.15 Tm
(of )Tj
0.05 Tc 10.1089 0 0 9.4 264.76 355.15 Tm
(the )Tj
9.7133 0 0 9.4 283.43 355.15 Tm
(Italian )Tj
0.0295 Tc 9.4 0 0 9.4 316.22 355.15 Tm
(Ministry )Tj
-0.0277 Tc 4.149 0 Td
(for )Tj
0.0191 Tc -35.879 -1.245 Td
(Research )Tj
0.05 Tc 9.7524 0 0 9.4 57.86 343.45 Tm
(and )Tj
0.0049 Tc 9.4 0 0 9.4 77.14 343.45 Tm
(Technology. )Tj
/T1_4 1 Tf
0.05 Tc 14.3852 0 0 13.3 18.46 311.77 Tm
(References )Tj
/T1_0 1 Tf
-0.035 Tc 7.4675 0 0 9.4 23.22 290.17 Tm
([1] )Tj
9.3087 0 0 9.4 37.75 290.17 Tm
(E. )Tj
0.0401 Tc 9.4 0 0 9.4 50.36 290.17 Tm
(Ballico )Tj
0.05 Tc 9.5174 0 0 9.4 83.6 290.17 Tm
(and )Tj
-0.035 Tc 9.2785 0 0 9.4 103.12 290.17 Tm
(A. )Tj
0.0194 Tc 9.4 0 0 9.4 116.72 290.17 Tm
(Cossidente, )Tj
0.0449 Tc 5.344 0 Td
(On )Tj
0.05 Tc 9.4259 0 0 9.4 183.22 290.17 Tm
(the )Tj
0.0152 Tc 9.4 0 0 9.4 199.7 290.17 Tm
(finite )Tj
-0.0123 Tc 2.643 0 Td
(field )Tj
0.0422 Tc 2.274 0 Td
(Nullstellensatz, )Tj
/T1_1 1 Tf
0.0033 Tc 9.6 0 0 9.6 314.97 290.17 Tm
(Australas. )Tj
-0.035 Tc 8.5139 0 0 10 359.55 290.17 Tm
(J. )Tj
-0.0002 Tc 9.6 0 0 9.6 38.51 278.47 Tm
(Gombin. )Tj
/T1_0 1 Tf
0.05 Tc 9.6015 0 0 9.2 76.62 278.47 Tm
(21 )Tj
0.0054 Tc 9.4 0 0 9.4 91.51 278.47 Tm
(\(2000\), )Tj
0.0302 Tc 3.368 0 Td
(57-60. )Tj
-0.035 Tc 7.4675 0 0 9.4 23.4 258.67 Tm
([2] )Tj
8.6986 0 0 9.4 37.96 258.67 Tm
(A. )Tj
0.0401 Tc 9.4 0 0 9.4 51.26 258.67 Tm
(Blokhuis )Tj
0.05 Tc 9.5174 0 0 9.4 92.06 258.67 Tm
(and )Tj
0.0199 Tc 9.4 0 0 9.4 111.15 258.67 Tm
(G.E. )Tj
0.0163 Tc 2.456 0 Td
(Moorhouse, )Tj
0.006 Tc 5.463 0 Td
(Some )Tj
0.038 Tc 2.681 0 Td
(p-ranks )Tj
0.0421 Tc 3.674 0 Td
(related )Tj
0.05 Tc 10.0407 0 0 9.4 277.9 258.67 Tm
(to )Tj
0.0403 Tc 9.4 0 0 9.4 290.43 258.67 Tm
(orthogonal )Tj
0.0068 Tc 5.128 0 Td
(spaces, )Tj
/T1_1 1 Tf
-0.035 Tc 8.5139 0 0 9.8 38.43 247.33 Tm
(J. )Tj
-0.0241 Tc 9.6 0 0 9.6 49.29 247.33 Tm
(Algebr-aic )Tj
0.0011 Tc 4.502 0 Td
(Combin. )Tj
/T1_0 1 Tf
0 Tc 9.4 0 0 9.4 129.74 247.33 Tm
(4 )Tj
-0.0009 Tc 0.988 0 Td
(\(1995\), )Tj
-0.03 Tc 3.337 0 Td
(295--316. )Tj
-0.035 Tc 7.4675 0 0 9.4 23.58 227.71 Tm
([3] )Tj
0.0263 Tc 9.4 0 0 9.4 38.07 227.71 Tm
(G.E. )Tj
0.0334 Tc 2.495 0 Td
(Moorhouse, )Tj
0.006 Tc 5.693 0 Td
(Some )Tj
0.05 Tc 9.5774 0 0 9.4 140.77 227.71 Tm
(p-ranks )Tj
0.0357 Tc 9.4 0 0 9.4 176.93 227.71 Tm
(related )Tj
0.0488 Tc 3.446 0 Td
(to )Tj
0.041 Tc 1.357 0 Td
(Hermitian )Tj
0.0396 Tc 4.847 0 Td
(varieties, )Tj
/T1_3 1 Tf
-0.035 Tc 8.4805 0 0 9.1 310.78 227.71 Tm
(J. )Tj
/T1_1 1 Tf
0.0057 Tc 9.6 0 0 9.6 322.73 227.71 Tm
(Stat. )Tj
-0.0212 Tc 2.446 0 Td
(Plan. )Tj
0.0188 Tc 9.2 0 0 9.2 38.43 216.01 Tm
(Inf. )Tj
/T1_0 1 Tf
0.05 Tc 9.9233 0 0 9.2 56.02 216.01 Tm
(56 )Tj
0.0182 Tc 9.4 0 0 9.4 70.99 216.01 Tm
(\(1996\), )Tj
0.0157 Tc 3.49 0 Td
(229-241 )Tj
-0.035 Tc 7.2978 0 0 9.4 23.95 197.11 Tm
([4] )Tj
0.0199 Tc 9.4 0 0 9.4 38.43 197.11 Tm
(G.E. )Tj
0.0312 Tc 2.361 0 Td
(Moorhouse, )Tj
0.006 Tc 5.539 0 Td
(Some )Tj
0.05 Tc 9.5774 0 0 9.4 137.17 197.11 Tm
(p-ranks )Tj
0.0357 Tc 9.4 0 0 9.4 172.25 197.11 Tm
(related )Tj
0.05 Tc 9.6041 0 0 9.4 203.2 197.11 Tm
(to )Tj
0.0152 Tc 9.4 0 0 9.4 214.46 197.11 Tm
(finite )Tj
0.0317 Tc 2.587 0 Td
(geometric )Tj
0.0487 Tc 4.61 0 Td
(structures, )Tj
0.0051 Tc 5.041 0 Td
(in )Tj
/T1_1 1 Tf
-0.0041 Tc 9.6 0 0 9.6 340.84 197.11 Tm
(Mostly )Tj
0.0207 Tc -31.465 -1.2 Td
(Finite )Tj
0.0209 Tc 2.991 0 Td
(Geometries, )Tj
/T1_0 1 Tf
-0.0217 Tc 9.4 0 0 9.4 119.96 185.59 Tm
(ed. )Tj
-0.0107 Tc 1.662 0 Td
(N.L. )Tj
0.0251 Tc 2.269 0 Td
(Johnson, )Tj
0.0186 Tc 4.176 0 Td
(Marcel )Tj
0.0164 Tc 3.294 0 Td
(Dekker )Tj
0.0288 Tc 3.424 0 Td
(Inc., )Tj
0.0155 Tc 2.385 0 Td
(1997, )Tj
0.0159 Tc 2.704 0 Td
(353-364. )Tj
-0.035 Tc 7.4675 0 0 9.4 23.94 165.79 Tm
([5] )Tj
8.8136 0 0 9.4 38.66 165.79 Tm
(P. )Tj
0.0361 Tc 9.4 0 0 9.4 50.49 165.79 Tm
(Griffiths )Tj
0.05 Tc 9.5174 0 0 9.4 89.9 165.79 Tm
(and )Tj
9.5175 0 0 9.4 109.21 165.79 Tm
(J. )Tj
0.0291 Tc 9.4 0 0 9.4 120.56 165.79 Tm
(Harris, )Tj
/T1_1 1 Tf
0.0094 Tc 9.6 0 0 9.6 153.25 165.79 Tm
(Principles )Tj
0.05 Tc 9.8154 0 0 9.6 198.46 165.79 Tm
(of )Tj
-0.0043 Tc 9.6 0 0 9.6 209.85 165.79 Tm
(Algebraic )Tj
0.0203 Tc 4.408 0 Td
(Geometry, )Tj
/T1_0 1 Tf
0.0063 Tc 9.4 0 0 9.4 299.34 165.79 Tm
(\\Viley )Tj
0.05 Tc 9.5174 0 0 9.4 327.14 165.79 Tm
(and )Tj
-0.0087 Tc 9.4 0 0 9.4 346.33 165.79 Tm
(Sons, )Tj
-0.0133 Tc -32.743 -1.206 Td
(1978. )Tj
-0.035 Tc 7.6372 0 0 9.4 23.94 135.01 Tm
([6] )Tj
0.0011 Tc 9.4 0 0 9.4 38.65 135.01 Tm
(J. )Tj
0.0483 Tc 1.265 0 Td
(Harris, )Tj
/T1_1 1 Tf
-0.0019 Tc 9.6 0 0 9.6 85.65 135.01 Tm
(Algebraic )Tj
0.0086 Tc 4.502 0 Td
(Geometry, )Tj
0 Tc 4.948 0 Td
(A )Tj
0.0239 Tc 1.23 0 Td
(First )Tj
-0.0057 Tc 2.634 0 Td
(Course, )Tj
/T1_0 1 Tf
0.0328 Tc 9.4 0 0 9.4 249.31 135.01 Tm
(Springer-Verlag, )Tj
-0.0244 Tc 7.835 0 Td
(New )Tj
-0.0143 Tc 2.387 0 Td
(York, )Tj
-0.0133 Tc -32.624 -1.264 Td
(1992. )Tj
-0.035 Tc 7.2978 0 0 9.4 24.31 104.05 Tm
([7] )Tj
0.0447 Tc 9.4 0 0 9.4 38.83 104.05 Tm
(J.W.P. )Tj
0.0242 Tc 3.295 0 Td
(Hirschfeld )Tj
0.0308 Tc 4.781 0 Td
(and )Tj
0.0338 Tc 1.882 0 Td
(J.A. )Tj
0.0402 Tc 2.084 0 Td
(Thas, )Tj
/T1_1 1 Tf
-0.0017 Tc 9.6 0 0 9.6 178.55 104.05 Tm
(General )Tj
-0.004 Tc 3.619 0 Td
(Galois )Tj
-0.0181 Tc 3.038 0 Td
(Geometr-ies, )Tj
/T1_0 1 Tf
0.032 Tc 9.4 0 0 9.4 294.39 104.05 Tm
(Oxford )Tj
0.017 Tc 3.36 0 Td
(University )Tj
0.0213 Tc -30.546 -1.226 Td
(Press, )Tj
0.0392 Tc 2.944 0 Td
(Oxford, )Tj
-0.0181 Tc 3.843 0 Td
(1991. )Tj
/T1_1 1 Tf
0.05 Tc 9.8965 0 0 9.6 142.54 40.69 Tm
(\(Received )Tj
10.0038 0 0 9.6 192.06 40.69 Tm
(17/11/2000\) )Tj
/T1_0 1 Tf
-0.023 Tc 9.4 0 0 9.4 187.09 15.48 Tm
(315 )Tj
ET
endstream
endobj
72 0 obj
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(1.1 )Tj
/T1_2 1 Tf
0.005 Tc 9.8 0 0 9.8 96.94 488.71 Tm
(Let )Tj
0 Tc 1.659 0 Td
(G )Tj
/T1_4 1 Tf
7.5001 0 0 7.5001 124.45 488.71 Tm
(C )Tj
/T1_0 1 Tf
-0.0007 Tc 7.1 0 0 7.1 134.81 488.71 Tm
(jpN )Tj
/T1_2 1 Tf
-0.035 Tc 8.1159 0 0 9.8 151.14 488.71 Tm
(be )Tj
-0.0192 Tc 9.8 0 0 9.8 162.78 488.71 Tm
(the )Tj
-0.0067 Tc 1.637 0 Td
(Pliicker )Tj
-0.0161 Tc 3.564 0 Td
(embedding )Tj
0.05 Tc 9.8154 0 0 9.2 259.84 488.71 Tm
(of )Tj
9.7382 0 0 9.2 271.38 488.71 Tm
(any )Tj
-0.0093 Tc 9.8 0 0 9.8 291.04 488.71 Tm
(Grassmannian. )Tj
0.0111 Tc 6.759 0 Td
(Then )Tj
-0.0192 Tc -33.127 -1.212 Td
(the )Tj
-0.0004 Tc 1.589 0 Td
(pair )Tj
-0.0248 Tc 1.985 0 Td
(\(G, )Tj
0.0008 Tc 1.543 0 Td
(G\(q\)\) )Tj
0.0001 Tc 2.723 0 Td
(satisfies )Tj
-0.0065 Tc 3.623 0 Td
(FFN\(q\). )Tj
/T1_3 1 Tf
0.05 Tc 9.9032 0 0 9.3 32.35 456.13 Tm
(Remark )Tj
9.7752 0 0 9.3 73.79 456.13 Tm
(1.2 )Tj
/T1_0 1 Tf
9.3482 0 0 9.3 91.9 456.13 Tm
(Theorem )Tj
-0.035 Tc 9.255 0 0 9.3 131.44 456.13 Tm
(1.1 )Tj
-0.0305 Tc 9.3 0 0 9.3 145.36 456.13 Tm
(is )Tj
0.05 Tc 9.3857 0 0 9.3 153.77 456.13 Tm
(sharp )Tj
0.0296 Tc 9.3 0 0 9.3 178.93 456.13 Tm
(because )Tj
/T1_1 1 Tf
-0.035 Tc 9 0 0 9 212.97 456.13 Tm
(pN )Tj
8.9156 0 0 9.6 225.86 456.13 Tm
(\(q\) )Tj
/T1_0 1 Tf
-0.0111 Tc 9.3 0 0 9.3 239.68 456.13 Tm
(is )Tj
0.05 Tc 9.5625 0 0 9.3 248.56 456.13 Tm
(the )Tj
9.4492 0 0 9.3 264.06 456.13 Tm
(union )Tj
0.039 Tc 9.3 0 0 9.3 290.43 456.13 Tm
(of )Tj
0.05 Tc 9.4259 0 0 9.3 300.4 456.13 Tm
(the )Tj
9.5823 0 0 9.3 315.62 456.13 Tm
(GF\(q\)-rational )Tj
0.0435 Tc 9.3 0 0 9.3 32.41 444.61 Tm
(points )Tj
0.05 Tc 9.3902 0 0 9.3 60.75 444.61 Tm
(of )Tj
/T1_2 1 Tf
0 Tc 9.8 0 0 9.8 71.76 444.61 Tm
(q )Tj
/T1_4 1 Tf
12.5 0 0 12.5 78.46 444.61 Tm
(+ )Tj
/T1_0 1 Tf
9.3 0 0 9.3 88.24 444.61 Tm
(1 )Tj
0.0363 Tc 0.827 0 Td
(hyperplanes )Tj
0.0151 Tc 5.585 0 Td
(defined )Tj
0.0019 Tc 3.503 0 Td
(over )Tj
/T1_2 1 Tf
0.0385 Tc 9.8 0 0 9.8 200.5 444.61 Tm
(GF\(q\). )Tj
/T1_0 1 Tf
0.0111 Tc 9.3 0 0 9.3 234.86 444.61 Tm
(Hence, )Tj
0.0364 Tc 3.303 0 Td
(for )Tj
0.0292 Tc 1.704 0 Td
(any )Tj
0.0221 Tc 1.892 0 Td
(subvariety )Tj
/T1_2 1 Tf
0 Tc 9.8 0 0 9.8 343.46 444.61 Tm
(X )Tj
/T1_0 1 Tf
-0.0191 Tc 9.3 0 0 9.3 354.69 444.61 Tm
(of )Tj
/T1_1 1 Tf
0.045 Tc 9 0 0 9 365.07 444.61 Tm
(pN )Tj
/T1_0 1 Tf
0.0151 Tc 9.3 0 0 9.3 32.67 432.91 Tm
(defined )Tj
0.0083 Tc 3.484 0 Td
(over )Tj
/T1_2 1 Tf
0 Tc 9.8 0 0 9.8 85.48 432.91 Tm
[(G )190(F )]TJ
/T1_0 1 Tf
1.569 0 Td
(\( )Tj
/T1_2 1 Tf
0.318 0 Td
(q )Tj
/T1_0 1 Tf
-0.035 Tc 9.5257 0 0 9.8 108.84 432.91 Tm
(\), )Tj
0.05 Tc 9.5625 0 0 9.3 118.06 432.91 Tm
(the )Tj
0.0402 Tc 9.3 0 0 9.3 134.29 432.91 Tm
(pair )Tj
/T1_1 1 Tf
0.05 Tc 9.296 0 0 8.8 153.85 432.91 Tm
(\(X, )Tj
0 Tc 8.8 0 0 8.8 169.47 432.91 Tm
(X )Tj
/T1_4 1 Tf
1.036 0 Td
(\( )Tj
/T1_2 1 Tf
-0.0155 Tc 9.8 0 0 9.8 181.56 432.91 Tm
(q\)\) )Tj
/T1_0 1 Tf
0.0219 Tc 9.3 0 0 9.3 196.73 432.91 Tm
(never )Tj
0.0424 Tc 2.729 0 Td
(has )Tj
0.05 Tc 9.4661 0 0 9.3 239.23 432.91 Tm
(property )Tj
9.6721 0 0 9.3 278.96 432.91 Tm
(FFN )Tj
/T1_2 1 Tf
-0.035 Tc 8.6667 0 0 9.8 298.63 432.91 Tm
(\(q )Tj
/T1_4 1 Tf
0 Tc 12.9 0 0 12.9 308.67 432.91 Tm
(+ )Tj
/T1_0 1 Tf
-0.035 Tc 9.1759 0 0 9.3 317.92 432.91 Tm
(1\). )Tj
0.0333 Tc 9.3 0 0 9.3 46.92 412.03 Tm
(In )Tj
0.0341 Tc 1.39 0 Td
(dealing )Tj
0.0482 Tc 3.628 0 Td
(with )Tj
0.0471 Tc 2.449 0 Td
(Grassmann )Tj
0.0184 Tc 5.396 0 Td
(spaces, )Tj
0.0321 Tc 3.59 0 Td
(Moorhouse )Tj
0.0327 Tc 5.338 0 Td
(in )Tj
-0.035 Tc 8.6539 0 0 9.3 262.41 412.03 Tm
([4, )Tj
0.0469 Tc 9.3 0 0 9.3 277.48 412.03 Tm
(Theorem )Tj
-0.035 Tc 6.9311 0 0 9.3 318.56 412.03 Tm
(2] )Tj
0.0118 Tc 9.3 0 0 9.3 329.41 412.03 Tm
(proved )Tj
0.05 Tc 10.3974 0 0 9.3 360.51 412.03 Tm
(that )Tj
9.411 0 0 9.3 32.9 400.69 Tm
(FFN\(q )Tj
0 Tc 9.3 0 0 9.3 63.25 400.69 Tm
(-)Tj
/T1_4 1 Tf
-0.035 Tc 8.6905 0 0 9.4 72.98 400.69 Tm
(1\) )Tj
/T1_0 1 Tf
-0.0305 Tc 9.3 0 0 9.3 84.7 400.69 Tm
(is )Tj
0.05 Tc 9.42 0 0 9.3 94.66 400.69 Tm
(true )Tj
-0.0023 Tc 9.3 0 0 9.3 114.74 400.69 Tm
(for )Tj
0.0492 Tc 1.615 0 Td
(the )Tj
0.0202 Tc 1.759 0 Td
(Pliicker )Tj
0.0426 Tc 3.671 0 Td
(embedding )Tj
0.05 Tc 9.3902 0 0 9.3 228.69 400.69 Tm
(of )Tj
0.0389 Tc 9.3 0 0 9.3 240.03 400.69 Tm
(any )Tj
0.05 Tc 9.3147 0 0 9.3 258.39 400.69 Tm
(Grassmannian. )Tj
9.5912 0 0 9.3 325.34 400.69 Tm
(Our )Tj
0.0452 Tc 9.3 0 0 9.3 345.04 400.69 Tm
(theorem )Tj
-0.0305 Tc -33.568 -1.239 Td
(is )Tj
0.0417 Tc 1.04 0 Td
(stronger )Tj
0.0468 Tc 4.018 0 Td
(then )Tj
0.0346 Tc 2.32 0 Td
(Moorhouse's )Tj
0.0324 Tc 5.887 0 Td
(result )Tj
0.0389 Tc 2.856 0 Td
(and )Tj
0.05 Tc 9.6991 0 0 9.3 201.04 389.17 Tm
(the )Tj
0.0425 Tc 9.3 0 0 9.3 217.89 389.17 Tm
(approach )Tj
-0.0305 Tc 4.433 0 Td
(is )Tj
0.0298 Tc 1.025 0 Td
(different. )Tj
-0.0054 Tc 4.59 0 Td
(In )Tj
0.0346 Tc 1.246 0 Td
(particular, )Tj
-0.035 Tc 8.838 0 0 9.3 368.79 389.17 Tm
([4, )Tj
0.05 Tc 9.3482 0 0 9.3 32.86 377.47 Tm
(Theorem )Tj
-0.035 Tc 7.6242 0 0 9.3 73.22 377.47 Tm
(2] )Tj
-0.0305 Tc 9.3 0 0 9.3 83.8 377.47 Tm
(is )Tj
0 Tc 1.025 0 Td
(a )Tj
0.0219 Tc 0.813 0 Td
(consequence )Tj
0.039 Tc 5.71 0 Td
(of )Tj
0.05 Tc 9.3019 0 0 9.3 164.62 377.47 Tm
(Theorem )Tj
0.0117 Tc 9.1 0 0 9.1 205.07 377.47 Tm
(1.1. )Tj
0.05 Tc 9.536 0 0 9.3 224.03 377.47 Tm
(In )Tj
9.5625 0 0 9.3 236.14 377.47 Tm
(the )Tj
0.0211 Tc 9.3 0 0 9.3 252.45 377.47 Tm
(case )Tj
0.05 Tc 10.0163 0 0 9.3 272.96 377.47 Tm
(of )Tj
9.5625 0 0 9.3 284.56 377.47 Tm
(the )Tj
0.0022 Tc 9.3 0 0 9.3 300.92 377.47 Tm
(Klein )Tj
0.0271 Tc 2.588 0 Td
(quadric, )Tj
0.05 Tc 10.3974 0 0 9.3 361.05 377.47 Tm
(that )Tj
-0.0048 Tc 9.3 0 0 9.3 33.04 365.59 Tm
(is, )Tj
-0.0023 Tc 1.314 0 Td
(for )Tj
0.05 Tc 9.5625 0 0 9.3 60.1 365.59 Tm
(the )Tj
0.023 Tc 9.3 0 0 9.3 76.46 365.59 Tm
(Pliicker )Tj
0.0378 Tc 3.671 0 Td
(embedding )Tj
0.039 Tc 5.111 0 Td
(of )Tj
0.05 Tc 9.4259 0 0 9.3 169.18 365.59 Tm
(the )Tj
9.3586 0 0 9.3 185.85 365.59 Tm
(Grassmannian )Tj
0.039 Tc 9.3 0 0 9.3 248.13 365.59 Tm
(of )Tj
0.0355 Tc 1.201 0 Td
(lines )Tj
0.0197 Tc 2.457 0 Td
(of )Tj
-0.035 Tc 7.9846 0 0 9.3 293.23 365.59 Tm
(jp3, )Tj
-0.0346 Tc 9.3 0 0 9.3 308.39 365.59 Tm
(see )Tj
-0.035 Tc 8.3255 0 0 9.3 323.62 365.59 Tm
([2]. )Tj
0.0012 Tc 9.3 0 0 9.3 340.52 365.59 Tm
(For )Tj
0.05 Tc 9.5136 0 0 9.3 356.85 365.59 Tm
(other )Tj
0.0364 Tc 9.3 0 0 9.3 33.11 353.71 Tm
(results )Tj
0.0268 Tc 3.224 0 Td
(on )Tj
0.05 Tc 9.5625 0 0 9.3 76.3 353.71 Tm
(the )Tj
9.3412 0 0 9.3 92.66 353.71 Tm
(Finite )Tj
0.033 Tc 9.3 0 0 9.3 120.38 353.71 Tm
(Field )Tj
0.0277 Tc 2.583 0 Td
(Nullstellensatz, )Tj
0.0042 Tc 7.008 0 Td
(see )Tj
/T1_4 1 Tf
-0.035 Tc 7.1492 0 0 10.7 225.76 353.71 Tm
([11. )Tj
/T1_0 1 Tf
0.0382 Tc 9.3 0 0 9.3 47.43 342.19 Tm
(Over )Tj
0.05 Tc 9.5625 0 0 9.3 70.9 342.19 Tm
(the )Tj
0.0463 Tc 9.3 0 0 9.3 87.22 342.19 Tm
(last )Tj
0.0269 Tc 1.915 0 Td
(decade, )Tj
0.0435 Tc 3.646 0 Td
(there )Tj
0.0242 Tc 2.556 0 Td
(have )Tj
0.0197 Tc 2.422 0 Td
(been )Tj
0.0484 Tc 2.359 0 Td
(numerous )Tj
0.05 Tc 9.4888 0 0 9.3 250.93 342.19 Tm
(papers, )Tj
0.0498 Tc 9.3 0 0 9.3 285.1 342.19 Tm
(too )Tj
0.0163 Tc 1.781 0 Td
(many )Tj
0.05 Tc 9.6041 0 0 9.3 326.32 342.19 Tm
(to )Tj
0.015 Tc 9.3 0 0 9.3 338.23 342.19 Tm
(be )Tj
0.0464 Tc 1.344 0 Td
(quoted )Tj
0.0168 Tc -34.114 -1.277 Td
(here, )Tj
0.0341 Tc 2.43 0 Td
(dealing )Tj
0.0482 Tc 3.473 0 Td
(with )Tj
0.05 Tc 9.5625 0 0 9.3 109.42 330.31 Tm
(the )Tj
9.7264 0 0 9.3 124.93 330.31 Tm
(p-rank )Tj
0.0197 Tc 9.3 0 0 9.3 155.79 330.31 Tm
(of )Tj
0.0222 Tc 1.104 0 Td
(incidence )Tj
0.05 Tc 9.3198 0 0 9.3 206.62 330.31 Tm
(matrices )Tj
0.039 Tc 9.3 0 0 9.3 244.53 330.31 Tm
(of )Tj
0.0315 Tc 1.103 0 Td
(classes )Tj
0.039 Tc 3.329 0 Td
(of )Tj
0.0052 Tc 1.124 0 Td
(incidence )Tj
0.044 Tc 4.214 0 Td
(structures, )Tj
0.0236 Tc -32.477 -1.277 Td
(such )Tj
0.0307 Tc 2.385 0 Td
(as )Tj
0.0326 Tc 1.346 0 Td
(projective )Tj
0.0151 Tc 4.746 0 Td
(spaces, )Tj
0.05 Tc 9.394 0 0 9.3 144.7 318.43 Tm
(translation )Tj
0.0248 Tc 9.3 0 0 9.3 193.33 318.43 Tm
(planes, )Tj
0.048 Tc 3.473 0 Td
(orthogonal )Tj
0.028 Tc 5.221 0 Td
(spaces, )Tj
0.0116 Tc 3.567 0 Td
(generalized )Tj
0.0481 Tc 5.167 0 Td
(quad\255)Tj
0.025 Tc -34.617 -1.297 Td
(rangles, )Tj
0.0346 Tc 3.833 0 Td
(unitals, )Tj
0.0129 Tc 3.668 0 Td
(designs, )Tj
0.0469 Tc 3.857 0 Td
(Hermitian )Tj
0.0229 Tc 4.88 0 Td
(varieties, )Tj
0.05 Tc 9.4408 0 0 9.3 225.09 306.37 Tm
(Grassmann )Tj
0.0229 Tc 9.3 0 0 9.3 276.1 306.37 Tm
(varieties. )Tj
0.0272 Tc 4.56 0 Td
(Our )Tj
0.0246 Tc 2.06 0 Td
(result )Tj
0.0082 Tc 2.799 0 Td
(is )Tj
0 Tc 1.16 0 Td
(a )Tj
0.05 Tc 9.3426 0 0 9.3 33.57 294.85 Tm
(contribution )Tj
9.3858 0 0 9.3 86.92 294.85 Tm
(to )Tj
9.3215 0 0 9.3 97.65 294.85 Tm
(current )Tj
0.0142 Tc 9.3 0 0 9.3 130.31 294.85 Tm
(research )Tj
0.0268 Tc 3.785 0 Td
(on )Tj
0.05 Tc 9.3585 0 0 9.3 177.85 294.85 Tm
(p-ranks; )Tj
0.0261 Tc 9.3 0 0 9.3 215.81 294.85 Tm
(nevertheless, )Tj
0.0394 Tc 5.903 0 Td
(we )Tj
0.0198 Tc 1.54 0 Td
(consider )Tj
0.0211 Tc 3.813 0 Td
(our )Tj
0.0267 Tc 1.711 0 Td
(techniques )Tj
0 Tc -32.543 -1.219 Td
(a )Tj
0.0222 Tc 0.867 0 Td
(significant )Tj
0.05 Tc 9.344 0 0 9.3 86.81 283.51 Tm
(step )Tj
0.0339 Tc 9.3 0 0 9.3 107.08 283.51 Tm
(toward )Tj
0.0492 Tc 3.387 0 Td
(the )Tj
0.05 Tc 9.6721 0 0 9.3 154.94 283.51 Tm
(FFN )Tj
0.0368 Tc 9.3 0 0 9.3 177.49 283.51 Tm
(problem )Tj
-0.0023 Tc 3.956 0 Td
(for )Tj
0.05 Tc 9.433 0 0 9.3 229.23 283.51 Tm
(other )Tj
0.0358 Tc 9.3 0 0 9.3 254.14 283.51 Tm
(varieties, )Tj
0.0003 Tc 4.414 0 Td
(which )Tj
-0.035 Tc 8.4759 0 0 9.3 321.65 283.51 Tm
(we )Tj
-0.0341 Tc 9.3 0 0 9.3 335.24 283.51 Tm
(feel )Tj
0.0134 Tc 1.829 0 Td
(has )Tj
0.05 Tc 9.7155 0 0 9.3 369.08 283.51 Tm
(an )Tj
0.0475 Tc 9.3 0 0 9.3 33.76 271.99 Tm
(independent )Tj
0.034 Tc 5.768 0 Td
(interest. )Tj
/T1_3 1 Tf
0 Tc 13.7 0 0 13.7 34.46 240.31 Tm
(2 )Tj
0.05 Tc 14.9708 0 0 13.7 57.62 240.31 Tm
(The )Tj
14.921 0 0 13.7 89.71 240.31 Tm
(Proof )Tj
15.0506 0 0 13.7 132.5 240.31 Tm
(of )Tj
14.4869 0 0 13.7 150.15 240.31 Tm
(Theorem )Tj
0.0467 Tc 13.7 0 0 13.7 217.17 240.31 Tm
(1.1 )Tj
/T1_0 1 Tf
0.0205 Tc 9.3 0 0 9.3 34.34 218.89 Tm
(For )Tj
0.0389 Tc 1.949 0 Td
(any )Tj
0.0262 Tc 2.053 0 Td
(integers )Tj
/T1_2 1 Tf
0.0146 Tc 9.8 0 0 9.8 107.75 218.89 Tm
(x, )Tj
0.05 Tc 9.4167 0 0 9.2 120.37 218.89 Tm
(n, )Tj
/T1_0 1 Tf
0.0417 Tc 9.3 0 0 9.3 133.19 218.89 Tm
(with )Tj
0 Tc 21.4 0 0 21.4 155.58 218.89 Tm
(\260 )Tj
-0.035 Tc 8.1087 0 0 21.4 165.76 218.89 Tm
(::; )Tj
/T1_2 1 Tf
0 Tc 9.8 0 0 9.8 177.77 218.89 Tm
(x )Tj
/T1_4 1 Tf
10.6 0 0 10.6 188.65 218.89 Tm
(< )Tj
/T1_2 1 Tf
0.0489 Tc 9.2 0 0 9.2 199.93 218.89 Tm
(n, )Tj
/T1_0 1 Tf
0.0414 Tc 9.3 0 0 9.3 213.22 218.89 Tm
(let )Tj
/T1_2 1 Tf
0.0424 Tc 9.8 0 0 9.8 228.22 218.89 Tm
(G\(x, )Tj
0.05 Tc 9.5533 0 0 9.2 249.07 218.89 Tm
(n\) )Tj
/T1_0 1 Tf
9.335 0 0 9.3 263.17 218.89 Tm
(be )Tj
9.4259 0 0 9.3 278.26 218.89 Tm
(the )Tj
0.036 Tc 9.3 0 0 9.3 295.65 218.89 Tm
(Grassmannian )Tj
0.0003 Tc 6.619 0 Td
(of )Tj
/T1_2 1 Tf
0.05 Tc 11.8601 0 0 9.8 369.49 218.89 Tm
(x\255)Tj
/T1_0 1 Tf
0.0352 Tc 9.3 0 0 9.3 34.29 207.73 Tm
(dimensional )Tj
0.0326 Tc 5.585 0 Td
(projective )Tj
0.0284 Tc 4.655 0 Td
(linear )Tj
0.0311 Tc 2.762 0 Td
(subspaces )Tj
0.0003 Tc 4.63 0 Td
(of )Tj
/T1_2 1 Tf
-0.0131 Tc 9.8 0 0 9.8 208.95 207.73 Tm
(pn, )Tj
/T1_0 1 Tf
0.0183 Tc 9.3 0 0 9.3 226.4 207.73 Tm
(Hence )Tj
/T1_2 1 Tf
0.05 Tc 9.8519 0 0 9.8 254.29 207.73 Tm
(dim\(G\(x, )Tj
/T1_1 1 Tf
-0.0025 Tc 9.6 0 0 9.6 295.65 207.73 Tm
(n\)\) )Tj
/T1_4 1 Tf
0 Tc 8.1 0 0 8.1 311.27 207.73 Tm
(= )Tj
/T1_1 1 Tf
-0.035 Tc 8.865 0 0 9.6 320.9 207.73 Tm
(\(n )Tj
/T1_4 1 Tf
0 Tc 9.6 0 0 9.6 331.47 207.73 Tm
(-)Tj
/T1_2 1 Tf
-0.035 Tc 8.5834 0 0 9.8 340.05 207.73 Tm
(:r;\)\(x )Tj
/T1_4 1 Tf
0 Tc 11.7 0 0 11.7 359.45 207.73 Tm
(+ )Tj
/T1_0 1 Tf
0.0168 Tc 9.3 0 0 9.3 368.68 207.73 Tm
(1\). )Tj
0.05 Tc 9.763 0 0 9.3 34.67 196.57 Tm
(It )Tj
9.5054 0 0 9.3 44.8 196.57 Tm
(turns )Tj
9.686 0 0 9.3 69.39 196.57 Tm
(out )Tj
10.0691 0 0 9.3 86.38 196.57 Tm
(that )Tj
/T1_1 1 Tf
-0.035 Tc 8.5278 0 0 9.6 106.68 196.57 Tm
(G\(O, )Tj
9.2475 0 0 9.6 126.81 196.57 Tm
(n\) )Tj
/T1_0 1 Tf
0 Tc 12.4 0 0 12.4 138.72 196.57 Tm
(= )Tj
-0.035 Tc 7.6167 0 0 9.3 148.68 196.57 Tm
(jpn )Tj
0.05 Tc 9.3999 0 0 9.3 162.08 196.57 Tm
(and )Tj
/T1_1 1 Tf
0.0177 Tc 9.6 0 0 9.6 180.27 196.57 Tm
(G\(n )Tj
/T1_0 1 Tf
-0.0205 Tc 9.3 0 0 9.3 209.2 196.57 Tm
(1, )Tj
/T1_1 1 Tf
-0.0282 Tc 9.6 0 0 9.6 218.07 196.57 Tm
(n\) )Tj
/T1_0 1 Tf
0 Tc 12.4 0 0 12.4 230.52 196.57 Tm
(= )Tj
/T1_2 1 Tf
-0.035 Tc 9.0303 0 0 9.8 240.6 196.57 Tm
(pn* )Tj
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