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Birkenhake C., Lange H. — Complex Abelian Varieties
Birkenhake C., Lange H. — Complex Abelian Varieties



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Название: Complex Abelian Varieties

Авторы: Birkenhake C., Lange H.

Аннотация:

May be used as an introduction or reference. Covers the theory of abelian varieties over the field of complex numbers. Topics include projective embeddings of an abelian variety including their equations and geometric properties, special results of Jacobians and Prym varieties allowing applications to the theory of algebraic curves, complex tori, cohomology of line bundles, and constructions of several moduli spaces of abelian varieties with additional structure. Problems follow each chapter.


Язык: en

Рубрика: Математика/Алгебра/Алгебраическая геометрия/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2004

Количество страниц: 655

Добавлена в каталог: 12.03.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$16_6$-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 $Pic_0(M)$      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 $(—1)_x$      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 $(N_p)$      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 $e_H$      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-$\Theta$-regular sheaf      519
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