Complex Abelian Varieties

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Springer Science & Business Media, Apr 22, 2004 - Mathematics - 638 pages
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This book explores the theory of abelian varieties over the field of complex numbers, explaining both classic and recent results in modern language. The second edition adds five chapters on recent results including automorphisms and vector bundles on abelian varieties, algebraic cycles and the Hodge conjecture. ". . . far more readable than most . . . it is also much more complete." Olivier Debarre in Mathematical Reviews, 1994.

 

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Contents

IV
7
VI
9
VII
13
VIII
15
IX
21
X
23
XI
24
XII
29
XCVI
304
XCVII
308
XCVIII
310
XCIX
315
C
316
CI
322
CII
325
CIV
327

XIII
32
XIV
34
XV
37
XVI
41
XVII
45
XVIII
46
XIX
49
XX
54
XXI
56
XXII
61
XXIII
64
XXIV
66
XXV
69
XXVI
70
XXVII
73
XXVIII
74
XXIX
81
XXX
84
XXXI
88
XXXII
92
XXXIII
97
XXXIV
100
XXXV
102
XXXVI
105
XXXVII
109
XXXVIII
113
XXXIX
114
XL
119
XLI
122
XLII
128
XLIII
131
XLIV
140
XLV
145
XLVI
146
XLVII
149
XLVIII
151
XLIX
153
L
156
LI
159
LII
164
LIII
166
LIV
169
LV
174
LVI
179
LVII
180
LVIII
184
LIX
187
LX
190
LXI
196
LXII
198
LXIII
203
LXIV
209
LXV
210
LXVI
213
LXVII
216
LXVIII
217
LXIX
218
LXX
219
LXXI
220
LXXII
222
LXXIII
227
LXXIV
229
LXXV
232
LXXVI
234
LXXVII
235
LXXVIII
239
LXXIX
243
LXXX
245
LXXXI
246
LXXXII
251
LXXXIII
254
LXXXIV
257
LXXXV
262
LXXXVI
267
LXXXVII
270
LXXXVIII
274
LXXXIX
279
XC
281
XCI
282
XCII
285
XCIII
290
XCIV
293
XCV
300
CV
330
CVI
333
CVII
335
CVIII
337
CIX
341
CX
344
CXI
347
CXII
353
CXIII
359
CXIV
363
CXV
364
CXVI
368
CXVII
372
CXVIII
374
CXIX
378
CXX
381
CXXI
385
CXXII
388
CXXIII
394
CXXIV
399
CXXV
406
CXXVI
411
CXXVII
412
CXXVIII
413
CXXIX
417
CXXX
421
CXXXI
428
CXXXII
431
CXXXIII
436
CXXXIV
439
CXXXV
440
CXXXVI
444
CXXXVII
448
CXXXVIII
453
CXXXIX
455
CXL
459
CXLI
464
CXLII
469
CXLIII
476
CXLIV
479
CXLV
480
CXLVI
484
CXLVII
488
CXLVIII
491
CXLIX
496
CL
503
CLI
507
CLII
512
CLIII
517
CLIV
521
CLV
522
CLVI
525
CLVII
527
CLVIII
532
CLIX
534
CLX
538
CLXI
543
CLXII
546
CLXIII
549
CLXIV
550
CLXV
552
CLXVI
554
CLXVII
559
CLXVIII
561
CLXIX
564
CLXX
567
CLXXI
571
CLXXII
577
CLXXIV
578
CLXXV
579
CLXXVI
580
CLXXVIII
583
CLXXX
587
CLXXXI
589
CLXXXII
591
CLXXXIII
597
CLXXXV
599
CLXXXVI
601
CLXXXVII
603
CLXXXVIII
625
CLXXXIX
631
Copyright

Other editions - View all

Complex Abelian Varieties
Herbert Lange,Christina Birkenhake
Limited preview - 2013
Complex Abelian Varieties
Christina Birkenhake,Herbert Lange
Limited preview - 2013
Complex Abelian Varieties
Christina Birkenhake,Herbert Lange
No preview available - 2010
View all »

Common terms and phrases

abelian subvariety abelian surface According to Lemma According to Proposition algebraically equivalent ample line bundle analytic representation anti-involution automorphism canonical theta functions characteristic coherent sheaf cohomology completes the proof complex torus consider Corollary corresponding curve of genus decomposition defined denote dimension g double covering element elliptic curve embedding endomorphism structure Endq(X equation factor finite formula functor genus g Hence hermitian form Hodge homomorphism hyperelliptic implies the assertion induces integer intersection involution irreducible isogeny isomorphism Jacobian lattice linear system Math moduli space Moreover morphism multiplication nondegenerate notation NS(X Pic(X Poincare bundle polarized abelian variety positive definite principally polarized principally polarized abelian Prym variety Recall respect Section smooth projective curve subgroup subvector space suffices to show Suppose surjective symmetric line bundle symplectic basis theta divisor theta functions theta group theta structure unique variety of dimension vector bundle vector space

Popular passages

Page 4 - It is a pleasure to acknowledge the help and support we received from a number of people and institutions. In particular, we would like to thank
Appears in 2 books from 1999-2004

References to this book

Fourier-Mukai Transforms in Algebraic Geometry
Daniel Huybrechts
No preview available - 2006
Deformations of Algebraic Schemes
Edoardo Sernesi
Limited preview - 2007
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Bibliographic information

QR code for Complex Abelian Varieties
TitleComplex Abelian Varieties
Volume 302 of Grundlehren der mathematischen Wissenschaften
AuthorsChristina Birkenhake, Herbert Lange
Edition2, illustrated
PublisherSpringer Science & Business Media, 2004
ISBN3540204881, 9783540204886
Length638 pages
Subjects ›  › 

Mathematics / Algebra / General
Mathematics / Complex Analysis
Mathematics / Geometry / Algebraic
Mathematics / Mathematical Analysis
Mathematics / Number Theory
  
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