Hunt B. — Geometry of Some Special Arithmetic Quotients :: Электронная библиотека попечительского совета мехмата МГУ

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Hunt B. — Geometry of Some Special Arithmetic Quotients

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Название: Geometry of Some Special Arithmetic Quotients

Автор: Hunt B.

Язык:

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1996

Количество страниц: 356

Добавлена в каталог: 01.07.2008

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Предметный указатель

      47
Abelian surfaces, with a level 3 structure      217
Abelian varieties, level structure      27
Abelian variety      15 37 40 43 48 83 89 100 102 104 186 187 190
Abelian variety, as compactification divisor      199 202
Abelian variety, endomorphism algebra      15
Abelian variety, endomorphism ring      15
Abelian variety, moduli space of      19
Abelian variety, of type ${A, \Phi, *}$       17
Accessory irrationality      135 141 195 198
Adjunction      204
Algebraic equations      133
Algebraic group      265
Algebraic group, anisotropic      266
Algebraic group, isotropic      265
Algebraic group, of hermitian type      266
Arithmetic group      19 275—281
Arrangement      67 150 172 177 183 204 227 245
Arrangement, Fermat covers of      71
Arrangement, general position      68
Arrangement, induced      229
Arrangement, resolution      69
Arrangement, singular locus      68 71
Arrangement, singularities      68
Associated sets of lines      105
Baily — Borel embedding      87 105 197 203
Ball quotient      58 74 198—202 245
Ball quotient, Satake compactification of      220
Bergmann kernel function      201
Bergmann metric      63 201
Binary forms      297—302
Binary forms, discriminant      298
Binary forms, invariants      297
Binary forms, quintics      298
Binary forms, sextics      300
Binary sextic      157 195
Binary sextic, invariants      195
Binary sextic, Joubert normal form      162
Binary sextic, Maschke normal form      162
Binary sextic, Weierstrass form      159
Birational transformation      69 76 91 98 99
Boundary component      31 74 272—275
Boundary component, rational      273
Boundary varieties      52
Brauer group      257—259
Bring curve      143
Bring equation      139
Bring form      135
Burkhardt form problem      165
Burkhardt group      161 164 197 233
Burkhardt quartic $\mathcal{B}_4$       151 169—172
Burkhardt quartic $\mathcal{B}_4$ , dual variety      221
Burkhardt quartic $\mathcal{B}_4$ , Hessian variety      185 190 192
Burkhardt quartic $\mathcal{B}_4$ , modular subvarieties      219
Burkhardt quartic $\mathcal{B}_4$ , moduli interpretation      217 218
Burkhardt quartic $\mathcal{B}_4$ , rationality of      184
Calabi — Yau threefolds      241 243 247
Canonical level structure      41
Cayley cubic $\mathfrak{C}$       75 99 104 115—122
Cayley cubic $\mathfrak{C}$ , affine equation      117
Cayley cubic $\mathfrak{C}$ , Hessian variety      118 319
Cayley cubic $\mathfrak{C}$ , hexahedral form      115
Cayley cubic $\mathfrak{C}$ , lines      116
Cayley cubic $\mathfrak{C}$ , pentahedral form      115
Cayley cubic $\mathfrak{C}$ , tritangents      116
Central simple algebra      16 257
Central simple algebra, index      257
Central simple algebra, integral element      277
Central simple algebra, order      257
Central simple algebra, similar      257
Central simple algebra, splitting field      257
Class of a variety      288
Clebsch cubic $\mathfrak{C}$       75 122—128 143
Clebsch cubic $\mathfrak{C}$ , automorphism group      123
Clebsch cubic $\mathfrak{C}$ , Hessian      184 319
Clebsch cubic $\mathfrak{C}$ , hexahedral form      122
Clebsch cubic $\mathfrak{C}$ , lines      125
Clebsch cubic $\mathfrak{C}$ , pentahedral form      122
Clebsch cubic $\mathfrak{C}$ , tritangents      124
Clebsch transference principle      131 296 307
Coble variety $\mathfrak{Y}$       105—107 250
Coble variety $\mathfrak{Y}$ , modular subvarieties      106
Coble variety $\mathfrak{Y}$ , moduli interpretation      106
Coble variety $\mathfrak{Y}$ , singular locus      106
Collineation      310
Collineation group      165
Compactification      38
Compactification, Baily — Borel      216
Compactification, ball quotients      208
Compactification, Satake      36 45 78 104 216 218
Compactification, toroidal      36 45
Complex multiplication      83 104 218
Configuration, $(32_{10})$       103
Configuration,       311
Configuration, 15 lines      84
Configuration, 27 hyperplanes      241
Configuration, 36 points      232
Configuration, 45 nodes      172
Configuration, Hesse      174
Configuration, Witting      187
Correlation group      165
Covariant      294
Covariant, degree      284
Covariant, order      284
Covariant, projective      284
Covariant, weight      284
Cremona transformation      70 131 164
cube      68
Cubic line complex      313
Cubic surfaces      109—133 251
Cubic surfaces, covariant surface      307
Cubic surfaces, covariants      114
Cubic surfaces, degenerate      130
Cubic surfaces, discriminant      132
Cubic surfaces, double six      110 223 229
Cubic surfaces, double six, azygetic      111 224
Cubic surfaces, double six, syzygetic      111 224
Cubic surfaces, equation for the 27 lines      114 148—167
Cubic surfaces, equations      112
Cubic surfaces, equations, hexahedral      113
Cubic surfaces, equations, pentahedral      112
Cubic surfaces, Fermat      176
Cubic surfaces, Hessian variety      304 318
Cubic surfaces, hexahedral form      129 160
Cubic surfaces, invariants      114 131 302—310
Cubic surfaces, invariants, hexahedral      160 165
Cubic surfaces, invariants, irrational      163
Cubic surfaces, invariants, quatenary      160
Cubic surfaces, invariants, tritangent      164
Cubic surfaces, moduli space      105 107
Cubic surfaces, parabolic curve      304
Cubic surfaces, tritangents      110 223 227
Cubic surfaces, tritangents, triads of trihedral pairs      112 224
Cubic surfaces, tritangents, trihedral pair      111 224
Curvature      200
Cusp      45 99
Cyclic algebra      259
Cyclic algebra, with involution of the second kind      261
Defect      242
Del Pezzo surfaces      99 128—129
Desmic figure      68
Desmic surface      171 179
Desmic surface, double cover      181
Desmic surface, elliptic fibration      181
Desmic tetrahedra      171 175 179 233 311
Dieudonne determinant      29
Division algebra      16 29—31 259 280
Division problem      136
Domain      19
Domain, tube      31

Domain, type IV      46
Double octics      247
Duads      85
Dual variety      85 287
Dual variety, singularities of      288
Eckard point      123 164
Elementary symmetric functions      148 163 170 197 234 306 309
Elimination theory      155
Elliptic functions      139
Elliptic modular surface      49 55 93 203 220
Elliptic singularity      49
Enriques surface      317
Enveloping cone      192
Equation problem      132 160 290
Euler's theorem      291
Expressions of Lagrange      147
Fermat cover      49 71 93 204
Finite geometry      90
Form problem      133 150 290
Fox closure      71
Generating set for a group      216
GIT quotient      105
Hauptgleichung      142 148
Hauptmodul      137
Heisenberg group      100 188
Hermitian form      43 210 265
Hermitian form, anisotropic      260
Hermitian form, determinant      43
Hermitian form, involution of the first kind      256
Hermitian form, involution of the second kind      256
Hermitian form, isotropic      29 256
Hermitian form, over skew fields      255
Hermitian form, signature      43
Hesse group      151
Hesse pencil      150 174 203
Hesse pencil, extended      150
hessian      285
Hessian variety      285
Hessian variety, discriminant      284
Hilbert modular surface      75
Hodge structure      46
Hyperbolic planes      29—35 256 265
Hyperbolic planes, arithmetic groups      31 280
Hyperbolic planes, maximal isotropic subspaces      29
Hyperbolic planes, modular subvarieties      34
Hyperbolic planes, moduli interpretation      33
Hyperelliptic curves      56 153
Hyperelliptic curves, level structure      56
Hyperelliptic functions      148 186 218
Hypergeometric differential equation      72
Icosahedral equation      143
Icosahedral group $\mathfrak{I}$       123 175 301
Icosahedral solvent      147
icosahedron      143—149
Icosahedron, inscribed octahedron      143 147
Igusa desingularization      38 218
Igusa quartic $\mathfrak{I}_4$       84—94 163 249 319
Igusa quartic $\mathfrak{I}_4$ , Hessian variety      94
Igusa quartic $\mathfrak{I}_4$ , Jacobian ideal      92
Igusa quartic $\mathfrak{I}_4$ , moduli interpretation      89
Igusa quartic $\mathfrak{I}_4$ , singular locus      89
Invariant quintic $\mathfrak{I}_5$       234—239
Invariant quintic $\mathfrak{I}_5$ , as double cover      246
Invariant quintic $\mathfrak{I}_5$ , cuspidal model      244
Invariant quintic $\mathfrak{I}_5$ , equations      234
Invariant quintic $\mathfrak{I}_5$ , hyperplane sections      239
Invariant quintic $\mathfrak{I}_5$ , Jacobian ideal      237 242
Invariant quintic $\mathfrak{I}_5$ , Picard group      251
Invariant quintic $\mathfrak{I}_5$ , rationalization of      238
Invariant quintic $\mathfrak{I}_5$ , singularieties      236
Invariants      282—290
Invariants, absolute      283
Invariants, covariantly equivalent      133
Invariants, of finite groups      288
Invariants, relative      282
Invariants, simultaneous      282
Invariants, weight      283
Involution      255
Involution, canonical on quaternion algebra      260
Involution, of the second kind      16 30 259 261
Involution, orthogonal type      258
Involution, positive      15 264
Involution, Rosati      15
Involution, symplectic type      258 260
Isogeny      136
Isotropic subspaces      38 273 275
Isotropic subspaces, maximal      29
Jacobi equation      138
Jacobian determinant      191 285 289 315 317
Jacobian variety      52 83 219
Janus-like algebraic varieties      50—65 220
Jordan pentahedra      170
Jordan primes      151 171 173 179 219 233
K3-surfaces      47 105 107 188 192 193
K3-surfaces, degeneration      49
K3-surfaces, double covers      47
Killing form      226
Kummer modular surface      55 91
Kummer surface      48 86 89 100 180 190 193 217 219 310 315 319
Kummer surface, cone over      192
Lattice      17
Lattice, automorphisms of      19
Lattice, definite unimodular      45
Lattice, dual      41
Lattice, Picard      50
Lefschetz hyperplane theorem      77 251
Legendre normal form      138
Level a-structure      44
Level structure      20
Line coordinates      156
Logarithmic Chern classes      198
Macdonald representation      231
Maschke form problem      157 159
Maximal order      31
Metrics, dual      63
Mixed concomitants      287
Modular equation      135
Modular function      137
Moduli functors      22—25
Moduli spaces      22—28
Moduli spaces, coarse      25
Moduli spaces, fine      25
Moduli spaces, of abelian varieties      26
Moduli spaces, of complex abelian varieties      28
Mumford's proportionality      200
Nieto quintic $\mathcal{N}_5$       94 241
Nieto quintic $\mathcal{N}_5$ , moduli interpretation      100
Nieto quintic $\mathcal{N}_5$ , planes lying on      95
Nieto quintic $\mathcal{N}_5$ , singular locus      95
Node      48 69 86 99 102 115 118 170 188 203
Norm      277
Norm, reduced      29 257
octahedron      68
Order      275
Order of a variety      286
Order, discriminant      278
Order, maximal      277 279 281
Parabolic      59 207 275
Parabolic divisor      288
Parabolic, rational      31 272
Paramodular group      40
Pel-structure      20
Pel-type      20
Pel-type, admissible      21
Pel-type, equivalence of      20
Period      72 136 158 195 198 311
Period map      107 243
Period, normalized      19
Picard curves      55 219
Picard curves, level structure      56

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