Lange H., Birkenhake C. — Complex Tori :: Электронная библиотека попечительского совета мехмата МГУ

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Lange H., Birkenhake C. — Complex Tori

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Название: Complex Tori

Авторы: Lange H., Birkenhake C.

Аннотация:

This work is at the crossroads of a number of mathematical areas, including algebraic geometry, several complex variables, differential geometry, and representation theory. The authors, both expert mathematicians in the area of complex manifolds and representation theory, focus on complex tori, which are interesting for their own sake being the simplest of complex manifolds, and important in the theory of algebraic cycles via intermediate Jacobians. Although special complex tori, namely abelian varieties, have been investigated for nearly 200 years, not much is known about arbitrary complex tori.. "Complex Tori is aimed at the mathematician and graduate student and will be useful in the classroom or as a resource for self-study.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 251

Добавлена в каталог: 20.11.2009

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Предметный указатель

Abelian variety      36
Albanese variety      104 109
Algebraic dimension      55
Algebraic Griffiths intermediate Jacobian      114
Analytic norm      45
Analytic representation      4
Analytic trace      45
Analytically equivalent      6
Anti-involution of the first kind      116
Anti-involution of the second kind      116
Appell — Humbert Theorem      7
Back diagonal matrix      12
Backsymmetric      12
Canonical factor      6
Canonical factor of automorphy      66
Canonical theta functions      7
Center of a ring      226
Coarse moduli space      210
Complement of a subtorus      22
Complementary nondegenerate subtorus      52
Complex flag manifold      179
Complex structure      233
Complex structure in $O_{p,q}(\mathbb{R})$       235
Complex structure in $S_{p_{2g}}(\mathbb{R})$       233
Complex structure in $\alpha U_m(\mathbb{H})$       236
Complex torus      2
Degree of a homomorphism      5
Degree of imprimitivity      48
Differentiable theta functions      66
Division point      5
Dolbeault cohomology group      71
Dual complex torus      14
Dual homomorphism      15
Dual polarized complex torus      48
Embedding of nondegenerate complex tori      89
Endomorphism algebra      23 25
Endomorphism ring      23
Endomorphism structure      117
Euler — Poincare characteristic      8
EXPONENT      5
Exponent of a nondegenerate subtorus      49
Exponent of a polarization      44
Extension of complex tori      17
Factor      22 26
Family of complex tori      30 209
Fine moduli space      210
First Chern class      6
Flag domain      179
Flag manifold      179
Grassmanian variety of quotient vector spaces      128
Grassmannian variety of quotient vector spaces      31
Griffiths intermediate jacobian      97
Hamiltonian quaternions      228
Hard Lefschetz theorem      93
Harmonic forms      70
Hermitian metric on a line bundle      66
Hodge *-operator      65
Hodge decomposition      92
Hodge filtration      92
Hodge — Lefschetz triangle      98
Homomorphism of complex tori      3
Homomorphism of nondegenerate complex tori      37
Indecomposable complex torus      24 53
Index of a hermitian form      36
Index of a line bundle      36
Index of a polarization      36
Index of a real symmetric form      40
Index of a symmetric form      233
Induced polarization      37
Irreducible      53
Isogenous      5
Isogeny      5
Isomorphic      17
Kaehler metric      64
Kronecker product      225
Laplacian operator      68
Lazzeri intermediate Jacobian      110 111
Lefschetz decomposition      93

Lefschetz operator      93 100
Marking      208
Marking, $\mathcal{M}$ -marking      209
Maximal quotient abelian variety      57
Moduli functor      210
Moduli problem      208
Moduli space      207
Moduli space of all complex tori      215
Moduli space of nondegenerate complex tori      40 217
Moduli space, coarse      210
Moduli space, fine      210
Moduli space, topological coarse      211
Multiplication in an algebra F      117
Mumford's Index Theorem      72
N-division points      5
Negative definite subvector space      71
Neron — Severi group      6 9
Nondegenerate complex torus of index k      37
Nondegenerate complex torus with endomorphism structure      117 209
Nondegenerate complex torus with sympletctic basis      41
Nondegenerate line bundle      36
Nondegenerate reduction      39
Nondegenerate subtorus      49
Norm-endomorphism      49
Norm-endomorphism Criterion      50
Pair of complementary nondegenerate subtori      52
Period matrix      2
Picard number      9 13
Picard variety      104 109
Poincare bundle      16
Poincare bundle, universal property of      16
Polarization      36
Polarization of index k      36
Polarization, dual      48
Polarization, exponent of a      44
Polarization, induced      37
Polarization, primitive      48
Polarization, principal      36
Polarization, type of      36
Positive semidefinite line bundle      56
Primitive cohomology group      93
Primitive Griffiths intermediate Jacobian      105
Primitive line bundle      48
Primitive polarization      48
Principal polarization      36
Quatemionic antiunitary group      189
Quatemionic unitary group      193
Radical      25
Rational map      74
Rational norm      45
Rational representation      4
Rational trace      45
Reducible nondegenerate complex torus      53
Relative tangent bundle      209
Riemann — Roch Theorem, analytic      8
Riemann — Roch theorem, geometric      8
Rosati involution      44 116
Semicharacter      6
Semisimple algebra      25
Semisimplification      26
Shafarevich extension      23
Simple complex torus      23 53
Star operator      65 67 110
Symmetric endomorphism      46
Symmetric idempotent      51
Symplectic basis      40 234
Symplectic marking      208
Theta function, differentiable      66
Topological coarse moduli space      21
Translation      3
Type la      116 119 127
Type lb      116 121
Type ll      117 123
Type of a line bundle      8
Type of a polarization      36
Type of a polarization of index k      36
Type of the dual polarization      48
Unitary basis      71 234
Weil intermediate Jacobian      106 108

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