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Hirschfield J.W. — Projective Geometries over Finite Fields
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Íàçâàíèå: Projective Geometries over Finite FieldsÀâòîð: Hirschfield J.W. Àííîòàöèÿ: This book is an account of the combinatorics of projective spaces over a finite field, with special emphasis on one and two dimensions. With its successor volumes, Finite projective spaces over three dimensions (1985), which is devoted to three dimensions, and General Galois geometries
ßçûê: Ðóáðèêà: Ìàòåìàòèêà /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Ãîä èçäàíèÿ: 1980Êîëè÷åñòâî ñòðàíèö: 488Äîáàâëåíà â êàòàëîã: 22.05.2008Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Ïðåäìåòíûé óêàçàòåëü
(k,l)-set 70—71 (k,l)-span 70 (k,l; r, s; n, q)-set 70 (k,r; n,q)-set 70 (k; r,s; n, q)-set 70 (k;n)-arc 320—364 (k;n)-arc of type 321 (k;n)-arc of type m 321—322 (k;n)-arc, complete 373 (k;n)-arc, deficiency of a 345—355 (k;n)-arc, i-secant of a 320—321 (k;n)-arc, maximal 324—335 (k;n)-arc, of type (0, 1, n) 342—343 (k;n)-arc, of type (m,n) 335—345 (k;n)-arc, t-maximal 335 338—341 (k;n)-arc, t-minimal 338—341 (k;r)-arc 70 (k;r)-cap 70 a-arc 186—199 235 Absolutely irreducible primal 50 Absolutely irreducible primal, variety 51 Acnode 223 Affine space 37 332—335 Affine space, axioms for 38—40 Arc, Herraitian 329 337—341 343—345 Arc, maximal 324—335 Associated point 128 132—133 Automorphism of a field 1 4 Automorphism of a space 30 Axioms for affine space 38—40 Axioms for projective space 38—39 B-point 393—395 397—404 408—414 Base point 55 Basis for a coordinate system 32 Bezout's theorem 223 Bisecant 70 Bisecant of a k-arc 165 Block 57 Blocking set 366—385 Blocking set, k-arc derived 366—367 Blocking set, minimal 366—368 373 Brianchon hexagon 393 Brianchon hexagon, point 393—395 397—404 408—414 Camot's theorem 57—58 Canonical form for a Hermitian variety 98—99 Canonical form for a polarity 110—115 Canonical form for a projectivity 40—46 124—128 149—157 Canonical form for a quadric 98—102 104—107 Category of a polyomial 13 19—20 Category of an element 4 13 Ceva's theorem 60 Character of a field 19 Characteristic of a field 1 Chord of a k-set 70—71 Class of a cubic curve 252 Collineation 30 Collineation, group 40—41 244 419—424 Committee 366 373 Companion matrix 44 Complete k-arc 163 232—239 Complete K-set 70 Complete series 54 Complex conjugate points 50 Complex inflexion 249 271 Complex point 50 Component of a curve 221 Component of a curve, irregular 221 Component of a curve, linear 221 Component of a curve, regular 221 Component of a primal 50 Component of a variety 51 Cone 51 Configuration, collineation group of a 244 Configuration, permutation group of a 244 Configuration, projective group of a 244 conic 107 140—146 235—239 Conic, nucleus of a 143 Conic, projective group of a 143—144 156—157 Conjugacy classes in GL(2,q) 124—125 Conjugacy classes in GL(3,q) 149—152 Conjugacy classes in PGL(2tq) 124—128 Conjugacy classes in PGL(5,q) 149—157 Conjugacy classes, number of 42 61—62 Conjugate points 33 Conjugate points, primes 33 Coordinate of a line 166 Coordinate system 31—32 Coordinate, non-homogeneous 54 119 Coordinates, prime 32—33 Coordinates, tangential 32—33 Correlation 33 Cross-axis of a projectivity 161 Cross-ratio 22—23 119—120 Crunode 223 Cubic curve with an isolated double point 226 259—268 Cubic curve with nine inflexions 278—280 Cubic curve with no inflexions 308—311 Cubic curve with one inflexion 282—307 Cubic curve with three inflexions 280—282 Cubic curve, equations 13 16 18—22 Cubic curves 225—226 241—318 357—358 361—363 Cubic curves equianharmonic 253 277 Cubic curves general 254 277 Cubic curves harmonic 253 277 Cubic curves nodal 226 254—256 267—268 Cubic curves non-singular 270—318 Cubic curves nucleus of 241 Cubic curves number of points on 311—313 Cubic curves singular 254—268 Cubic curves superharmonic 253 Cubic curves, classification of non-singular 313—318 Cubic curves, classification of singular 266—268 Cubic curves, cuspidal 226 256—259 267—268 Curve 49 51 Curve, genus of a 226—227 Curve, Hermitian 146—148 227 243 Curve, sub-Hermitian 148—149 227 Curves, cubic 225—226 241—318 361—363 Cusp 223 Cyclic projectivity 74—96 155 d-secant 70 Degree of a primal 49 Degree of of a variety 51 Desargues's theox-em 160—161 Design 37 Diagonal points of a pentastigm 139—140 Diagonal points of a tetrastigm 138 Diagonal points of an n-stigm 139—140 Dickson's criterion 3 Dimension of a projective space 29 Dimension of a variety 51 Dimension of a vector space 29 Dimension of an affine space 37 Discriminant 3 10 Dual space 31 Duality, principle of 31 Elation 153 Elementary divisor 43—46 Elementary divisor, operation 43 Elliptic quadric 106—111 114—115 Equations, cubic 13 16 18—22 Equations, equianharmonic quartic 22 25—27 Equations, harmonic quartic 22 Equations, quadratic 3 13 Equations, quartic 13 16—18 22—27 Equianharmonic quartic equations 22 25—27 Equianharmonic tetrad 121—122 130—131 Equivalence of matrices 43 EXPONENT 6 Extended symbol of a linear transformation 45—46 Extended symbol of a projectivity 45—46 External line of a k-arc 163 External line of an oval (conic) 165—166 170—171 External line, point of a k-arc 201 Field 1 finite 1 Finite fields 1—27 Finite fields, addition tables for 425—429 First polar 245—246 FORM 49 Fundamental theorem of projective geometry 30—31 General linear group 41 419—424 Generalized quadrangle 37 Grade of a point 164 Group, collineation 40—41 244 419—424 Group, general linear 41 124—125 149—152 419—424 Group, isomorphisms 422—424 Group, order of a semi-linear 420—421 Group, permutation 244 Group, projective 40 124—128 149—157 244 419—424 Group, projective, orthogonal 110 143—144 156—157 419—424 Group, projective, pseudo symplectic 113 174 419—424 Group, projective, special linear 41 419—424 Group, projective, symplectic 113 419—424 Group, projective, unitary 110 147 419—424 Group, special linear 41 419—424 Harmonic 152 Harmonic homology 152 Harmonic homology, polar 248 Harmonic homology, quartic equation 22 Harmonic homology, separation 120 Harmonic homology, syntheme 129—130 Harmonic homology, tetrad 120—121 129—131 133—135 169—170 Harmonic homology, tetrad, negative 134—135 Harmonic homology, tetrad, positive 134—135 Hasse — Weil theorem 225—232 Hermitian arc 329 337—341 343—345 Hermitian curve 146—148 228—229 243 Hermitian polarity 35—36 110 147—148 Hermitian variety 97—100 102—103 110—111 115 Hermitian variety in the plane 146—148 Hermitian variety on a line 122—123 Hermitian variety, canonical form for a 98—99 Hermitian variety, degenerate 97 Hermitian variety, group of a 110 Hermitian variety, number of points on a 102—103 Hessian of a cubic curve 246 Hessian polynomial 18—22 Hessian, indeterminate 248 Hexagon 55 Hexagon, Brianchon 393 Hexagon, Pascal 394 Hexastigm 55 Hexastigms, number of, not on a conic 142—143 Homology 152 Hyperbolic quadric 106—111 114—115 Hypercompanion matrix 44 Hyperplane 29 Hypersurface 49 Ideal line 38 74 Ideal point 38 74 Imaginary point 50 Incidence of subspaces 29 Incidence structure 37—40 74 Index of a k-arc 201 205—206 Index of a point 164 Inflexion 222 Inflexion of a cubic 246—250 Inflexional line 277 Inflexional tangent 246 Inflexional triangle 271 277 Internal point of a conic 165—166 170—171 Internal point of a k-arc 201 Intersection cycle 253 Intersection multiplicity 52 223 Intersection of subspaces 30 Invariant factor 43—44 46 Invariant, absolute 278 308 Invariants of polynomials 10—27 Involution 126—128 Involution, elliptic 126—128 Involution, hyperbolic 126—128 Involution, improper 126—128 Involution, parabolic 126—128 Involution, proper 126—128 Irreducible primal 50 Irreducible variety 51 Isolated double point 222 Isomorphisms of groups 422—424 Join 30 k-arc 54—55 70 163—219 387—414 k-arc, bisecant of a 163 k-arc, complete 163 205—208 214—219 232—239 k-arc, external line of a 163 k-arc, external line of a, point of a 201 k-arc, grade of a point off a 164 k-arc, index of a 201 205—206 k-arc, index of a, of a point off a 164 k-arc, internal point of a 201 k-arc, rank of a 201 205—206 k-arc, rank of a, of a point off a 204 k-arc, symmetric 207 k-arc, uniform 212—214 k-arc, unisecant of a 163 166—168 k-arcs, number of 137 k-cap 70 k-fold spread 81 k-set 69—71 k-set, chord of a 70—71 k-set, complete 70 k-set, tangent to a 70 Lagrange's interpolation formula 2 Line 29 38 119—135 Line, Hermitian variety on a 122—123 Line, ideal 38 74 Line, inflexional 277 Line, polarity on a 123 Line, projectivity on a 119 124—128 Line, proper 74 Line, quadric on a 122 Line, tangent 52 Linear independence 29 Linear series 54 Linear subsystem 53 Linear system 53—60 Linear transformation, extended symbol of a 45—46 Linear transformation, order of a 48—49 Linear transformation, symbol of a 45—46 Lines, parallel 38 332—335 Meet of subspaces 30 Menelaus's theorem 57—58 Model point 225 Multiplicity of a point 52 222 n-arc 54—55 n-curve 359—364 n-curve, complete 360 n-curve, multiple point on an 359—361 n-curve, multiplicity of a point on an 359 n-curve, simple point on an 359 N-gram 54—55 n-point 54—55 n-side 54—55 n-stigm 54—55 n-stigms, number of 137 Net 53 Node 222 Non-Desarguesian plane 74 Non-homogeneous coordinate 54 119 Nucleus of a (q+1)-arc 164—165 Nucleus of a conic 143
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