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

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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:

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

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Предметный указатель

Reider's theorem      293
Relative duality      590
Representation of the theta group      153
Representation Schrodinger      164
Riemann constant      324
Riemann Equations      198
Riemann Relations      73
Riemann Singularity Theorem      325
Riemann Theorem      324
Riemann theta function      223
Riemann Theta Relation      197 206
Riemann — Roch Theorem for vector bundles      68
Riemann — Roch Theorem geometric      65
Riemann — Roch Theorem, analytic      64
Riemann — Roch Theorem, geometric version for curves      326
Rigidity lemma      100
Rosati involution      114
Rosenhain tetrahedron      288
Schottky — Jung Relations      406
Schrodinger representation      164
Seesaw Principle      569
Self-intersection number      65
Semi stable, $\mu$ -semistable      453
Semicharacter      29
Seshadri constant      488
Shimura variety (analytic)      273
Siegel upper half space      211
Signature      264
Singular hyperplane      311
Singular plane      286
Singularity, exceptional      384
Singularity, stable      384
Stable, $\mu$ -stable      471
Stable, coherent sheaf      592
Star-operator *      106
Stein factorization      12
Symmetric idempotent      123
Symmetric line bundle      34
Symplectic basis      46
Symplectic group      212
Syzygy-module      205
Tetragonal construction      388
Theorem of Abel — Jacobi      319
Theorem of deFranchis      407
Theorem of Lefschetz      84
Theorem of Narasimhan and Nori      142
Theorem of Recillas      385
Theorem of Reider      293
Theorem of Riemann      324
Theorem of Serre — Rosenlicht      174
Theorem of the Cube      42
Theorem of the Square      33

Theorem of Torelli      321 360
Theorem Stone — von Neumann      174
Theorem, Bertini      283
Theorem, Riemann's Singularity      325
Theorem, Seesaw      568
Theta characteristic      324
Theta characteristic, even      325
Theta characteristic, odd      325
Theta Characteristics      325
Theta divisor      317
Theta divisor, canonical      324
Theta divisor, singularity locus      325
Theta function      49
Theta function, canonical      49
Theta function, classical      50
Theta function, differentiate      57
Theta function, finite      165
Theta function,- Riemann      223
Theta group      149
Theta group of L      147
Theta group, extended      170
Theta null value      232
Theta regularity      519
Theta Relation      196
Theta Relations, cubic      198 202
Theta Relations, Riemann      197 206
Theta structure      161
Theta structure symmetric      171
Theta structure, compatible      166
Theta structure, extended      171
Theta transformation formula      222 227
Torelli Problem      313
Torelli Theorem for the Prym map      409
Trace, analytic      116
Trace, rational      116
Trace, reduced      131
Translation map      10
Type of a line bundle      46
Type of a polarization      70
Universal Property of the Abel — Prymmap      369 378
Universal Property of the Albanese torus      354
Universal Property of the Jacobian      330
Universal Property of the Poincare bundle      38
Vanishing theorem      60
Vector bundle, $\mu$ -semi-stable      296
Vector bundle, $\mu$ -semistable      453
Vector bundle, $\mu$ -stable      296 471
Vector bundle, homogeneous      468
Vector bundle, unipotent      447
Welters' Criterion      370
WIT-sheaf      445
Zarhin's trick      141

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