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Электронная библиотека Попечительского совета
механико-математического факультета
Московского государственного университета
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| Birkenhake C., Lange H. - Complex Abelian Varieties |
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| Предметный указатель |
 -Configuration 311
Abel - Jacobi map 319 320
Abel - Jacobi theorem 319
Abel - Prym map 369
Abelian scheme 597
Abelian scheme, dual 598
Abelian variety 70
Abelian variety, dual 70 122
Abelian variety, G-decomposable 428
Abelian variety, G-simple 28
Abelian variety, of CM-type 558
Abelian variety, of Weil-type 565
Abelian variety, polarized 70
Abelian variety, simple 126
Action, proper and discontinuous 215 568
Addition formula 203
Addition map 8
Adjoint ideal 581
Adjunction formula 282
Albanese map 354
Albanese torus 353
Albanese variety 332
Albanese, maximal dimension 513 579
Algebra, opposite 134
Algebra, quaternion 133
Algebra, totally definite quaternion 134
Algebra, totally indefinite quaternion 134
Algebraic classes 559
Algebraic complex analytic space 567
Algebraic cycle 106 128 522
Algebraic dimension 312
Algebraic equivalence of cycles 524
Algebraic equivalence of line bundles 88
Algebraic p-cycle 106 128
Algebraic, dimension 86
Analytic representation 10
Anti-involution of the first kind 133
Anti-involution of the second kind 133
Anti-involution, positive 132
Appell - Humbert Theorem 32
Automorphism group, finite 421
Automorphism group, maximal in the isogeny class 421
Automorphism group, reduced 340
Azygetic set of 2-division points 112
Bertini's theorem 79
Bidegree of a correspondence 334
Big divisor 578
Bogomolov's inequality 296
Canonical basis 46
Canonical factor 32
Canonical polarization of  356
Canonical polarization of J(C) 317
Canonical theta divisor 324
Canonical theta function 49
Characteristic 47
Characteristic polynomial 115
Characteristic polynomial, reduced 131
Characteristic, compatible 159
Chern character 68 590
Chern class 296 590
Chern first ~ class 24 41
Chow ring 523
Chow, Theorem of 568
Classical factor of automorphy 49 50
Classical theta function 50
CM-type 417
Cocycle relation 571
Commutator map 151
Complementary abelian subvariety 125
Complex multiplication 262 266
Complex structure 550
Complex torus 8
Correspondence 333 525
Correspondence, bidegree of a 334
Correspondence, equivalent 333
Criterion of Matsusaka - Ran 341
Cubic equations 203
Cubic Theta Relations 198 202
Curve, d-gonal 385
Curve, over S 601
Cycle map 525
Cycle, algebraic 522
Cycle, generating an abelian variety 341
Cycle, Weil-Hodge cycle 565
Decomposition for E 46 49
Decomposition for H 46 49
Decomposition for L 46 49
Decomposition of the lattice 219
Decomposition, compatible 157 159
Decomposition, Theorem 75
Degree of a homomorphism 12
Degree of a polarization 119
Derivative of v 84
Derived category 584
Desargues configuration 205
Divisor, big 578
Divisor, even 93
Divisor, nef 489 577
Divisor, odd 93
Divisor, symmetric 92
Dolbeault cohomology groups 56
Donagi's Tetragonal Construction 388
Dual abelian scheme 598
Dual complex torus 34
Dual Jacobian Variety 359
Dual lattice 34
Dual polarization 453
Elliptic curve 9
Elliptic involution 294
Endomorphism structure of a polarized abelian variety 245
Endomorphism, primitive 124
Endomorphism, symmetric 119
Endomorphism, totally positive 120
Equivalence, algebraic 524
Equivalence, analytic 39
Equivalence, linear 71
Equivalence, numerical 106
Equivalence, rational 523
Equivalence,homological 106
Euler - Poincare characteristic 64
Exponent of a Prym - Tyurin variety 368
Exponent of an abelian subvariety 122
Exponent of an isogeny 13
Exponential map 8
Factor of automorphy 24 571
Fay's Trisecant Identity 348
First Chern class 24 41
Formal moduli space 593
Fourier transform 445 528 532 599
Fourier transform, relative 600
Functor, pro-representable 592
Fundamental class 322
Fundamental system 112
G-acyclic complex 588
Gauss map 81
Gauss map, generalized 110
General type 579
Genus arithmetic 282
Gopel tetrahedron 289
Graph of a morphism 526
Green's operator 19
Hamiltonian quaternions 132
Harmonic form 19
Harmonic form with values in a line bundle 56
Heat equation 226
Heisenberg group 161
Heisenberg group, extended 171
Heisenberg group, normalizer 177
Hermitian form 29
Hermitian, metric 18 56
| Hilbert modular varieties 251
Hilbert polynomial 592
Hodge class 556
Hodge conjecture 559
Hodge decomposition 15
Hodge group 555
Hodge structure 22 550
Homological equivalence 525
Homomorphism 10
Homomorphism of polarized abelian varieties 70
Index of a line bundle 61
Intersection number 75
Intersection number of cycles 104
Intersection product 522
Invariant form 15
Invariant form of type (p,q) 17
Inverse Formula 90
Inverse Formula for Finite Theta Functions 177
Inversion theorem 445 465
Irregularity 353
Isogenous complex tori 13
Isogeny 12
Isogeny of type D 240
Isogeny Theorem 157
Isogeny Theorem for finite theta functions 168
Isogeny Theorem, hypotheses of the 159
Isomorphism of L over  90
Isomorphism of polarized abelian varieties with endomorphism structure 245
IT-sheaf 444
Iwasawa decomposition 241
Jacobian, relative 601
Jacobian, variety 317
Jets 490
Kahler manifold 18
Kahler, metric 18
Kanev's Criterion 394
Klein quartic 361
Kodaira dimension 508 579
Koszul complex 486
Kronecker product of matrices 244
Kummer surface 204 285
Kummer surface, self-duality 288
Kummer variety 97
Kummer variety, trisecants 344
Kunneth decomposition 539
Lefschetz number 412
Lefschetz Theorem 86
Lefschetz, Decomposition 107
Level D-structure 163
Level structure 161 217
Level structure, D-structure 217
Level structure, generalized level n-structure 218
Level structure, n-structure 218
Level structure, orthogonal level D-structure 234
Line bundle, algebraic equivalent 88
Line bundle, ample 85
Line bundle, index of 61
Line bundle, nef 489
Line bundle, nondegenerate 37
Line bundle, normally generated 187
Line bundle, positive definite 49
Line bundle, positive semidefinite 54
Line bundle, symmetric 34
Line bundle, totally symmetric 176
Line bundle, very ample 85
Log canonical 13
Maximal quotient abelian variety 110
Minimal length of a period 496
Moduli space of polarized abelian varieties with endomorphism structure 249 256 261 266
Moduli space, coarse 591
Moduli space, fine 591
Moduli space, formal 593
Moduli space, local 593
Moving Lemma 128
Multi-index 16
Multiplication by N 168
Multiplication formula 182
Multiplication map 180
Multiplicity of a curve at a point 488
Mumford's Index Theorem 67
N-division points 12
Nakai - Moishezon criterion 77
Nefdivior 577
Neron - Severi group 29
Neron - Severi group of a complex torus 42
Nondegenerate line bundle 37
Norm map 331
Norm, analytic 116
Norm, rational 116
Norm-endomorphism 123
Norm-endomorphism Criterion 124
Normalized isomorphism 90
Period matrix 9
Period matrix for J(C) 317
Period of X 313
Pfaffian 50
Pfaffian, reduced 55
Picard bundle 461
Picard functor 597
Picard number 312
Picard scheme 598
Picard sheaves 460
Picard torus 355
Picard variety 356
Picard, number 42
Poincare bundle 38
Poincare bundle of degree n for C 459
Poincare bundle, cohomology of the 67
Poincare bundle, of degree n for C 328
Poincare bundle, relative 598
Poincare bundle, universal property of the 38
Poincare Formula 322
Poincare Reducibility Theorem 67 125
Polarization 70
Polarization type 70
Polarization, canonical of J(C) 317
Polarization, degree of 119
Polarization, dual 122 453
Polarization, exponent of 114
Polarization, induced 70
Polarization, isomorphic 121
Polarization, principal 70
Polarized abelian variety with symplectic basis 211
Pontryagin product 21 102 530
Pontryagin product of sheaves 450
Pontryagin product relative 542
Prime form 348
Primitive form 107
Proper intersection 522
Property  484
Prym canonical map 380
Prym differential 379
Prym map 409
Prym variety, associated to a covering 373
Prym variety, generalized 368
Prym - Tyurin variety 368
Prym - Tyurin variety for a curve 368
Prym - Tyurin variety, exponent 368
Quadratic form associated to  94
Quaternion multiplication, totally definite 257
Quaternion multiplication, totally indefinite 254
Radical of H 55
Rational equivalence 523
Rational map 101
Rational representation 10
Rational singularities 581
Real multiplication 246
Real Riemann matrix 109 110
Real torus 21
Regularity, m- -regular sheaf 519
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