Complex tori:
Although special complex tori, namely abelian varieties, have been investigated for nearly 200 years, not much is known about arbitrary complex tori."--BOOK JACKET. "Complex Tori is aimed at the mathematician and graduate student and will be useful in the classroom or as a resource for sel...
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1999
|
| Schriftenreihe: | Progress in mathematics
177 |
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008703770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Zusammenfassung: | Although special complex tori, namely abelian varieties, have been investigated for nearly 200 years, not much is known about arbitrary complex tori."--BOOK JACKET. "Complex Tori is aimed at the mathematician and graduate student and will be useful in the classroom or as a resource for self-study."--BOOK JACKET |
| Umfang: | XV, 251 S. |
| ISBN: | 3764341033 0817641033 |
Internformat
MARC
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| 520 | |a Although special complex tori, namely abelian varieties, have been investigated for nearly 200 years, not much is known about arbitrary complex tori."--BOOK JACKET. "Complex Tori is aimed at the mathematician and graduate student and will be useful in the classroom or as a resource for self-study."--BOOK JACKET | ||
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Datensatz im Suchindex
| _version_ | 1819336064380174336 |
|---|---|
| adam_text | Contents
Introduction xi
1 Complex Tori 1
1 Homomorphisms of Complex Tori 2
2 Line Bundles 5
3 The Neron Severi Group 9
4 The Dual Complex Torus 14
5 Extensions of Complex Tori 17
6 Complementary Subtori and Shafarevich Extensions .... 22
7 Simple and Indecomposable Complex Tori 23
8 The Endomorphism Algebra of a Complex Torus 25
9 The Theorem of Oort and Zarhin 28
10 The Space of all Complex Tori of Dimension g 30
2 Nondegenerate Complex Tori 35
1 Polarizations of Index k 36
2 Moduli Spaces of Nondegenerate Complex Tori 40
3 The Rosati Involution 44
4 The Dual Polarization 47
5 Poincare s Reducibility Theorem for Nongenerate
Complex Tori 49
6 The Algebraic Dimension 55
7 Picard Number and Algebraic Dimension of Complex Tori
of Dimension 2 58
vi Contents
3 Embeddings into Projective Space 63
1 Kahler Theory of Line Bundles on Complex Tori 64
2 Harmonic Forms with Values in a Nondegenerate
Line Bundle 70
3 Maps Associated to a Nondegenerate Line Bundle 74
4 The Family of Abelian Varieties Associated to a
Nondegenerate Complex Torus 76
5 Some Properties of the Diffeomeorphism 7v_ : X — Xv_ . 83
6 The Rational C°° map tpLy_ :X +FN 89
4 Intermediate Jacobians 91
1 Primitive Cohomology of Kahler Manifolds 92
2 The Griffiths Intermediate Jacobian 94
3 Some Properties of the Griffiths
Intermediate Jacobian 100
4 The Weil Intermediate Jacobian 106
5 The Lazzeri Intermediate Jacobian 110
6 The Abelian Variety Associated to the Griffiths
Intermediate Jacobian 113
5 Families of Complex Tori 115
1 Complex Tori with Endomorphism Structure 116
2 The Index of a Complex Torus with Endomorphism
Structure 119
3 Complex Tori with Endomorphism Structure of Type la . 127
4 Complex Tori with Endomorphism Structure of Type Ib . 139
5 Complex Tori with Endomorphism Structure of Type II . . 160
6 The Parameter Spaces of Complex Tori
with Endomorphism Structure 179
1 The Space HgM 180
2 The Space Km 184
3 The Space CmJ 186
4 The Space Mm,k 189
5 The Space 7Vm,fc 192
6 The Space ftmj 195
7 The Space Sn 196
8 The Space Tn 198
9 The Space W(Pj9),j 199
10 The Space Vp q 202
7 Moduli Spaces 207
Contents vii
1 Moduli Problems 208
2 Homogeneous Spaces with Noncompact Stabilizer 211
3 The Moduli Space of all Complex Tori 215
4 Moduli Spaces of Nondegenerate Complex Tori 217
5 Moduli Spaces of Nondegenerate Complex Tori
with Endomorphism Structure 220
A The Kronecker Product 225
B Anti Involutions on R Algebras 229
C Complex Structures 233
1 Complex Structures in Sp2m(R) 233
2 Complex Structures in OP,,(R) 235
3 Complex Structures in aUm{B) 236
4 Complex Structures in £/„,_*,* (H) 238
References 241
Glossary of Notations 245
Index 249
|
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| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
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| id | DE-604.BV012798654 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T10:36:23Z |
| institution | BVB |
| isbn | 3764341033 0817641033 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008703770 |
| oclc_num | 41404664 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-703 DE-20 DE-11 DE-19 DE-BY-UBM |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-703 DE-20 DE-11 DE-19 DE-BY-UBM |
| physical | XV, 251 S. |
| publishDate | 1999 |
| publishDateSearch | 1999 |
| publishDateSort | 1999 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spellingShingle | Birkenhake, Christina Lange, Herbert Complex tori Progress in mathematics Tore (Géométrie) ram Variétés complexes ram Complex manifolds Torus (Geometry) Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Torus (DE-588)4185738-0 gnd Komplexer Torus (DE-588)4164907-2 gnd |
| subject_GND | (DE-588)4031996-9 (DE-588)4185738-0 (DE-588)4164907-2 |
| title | Complex tori |
| title_auth | Complex tori |
| title_exact_search | Complex tori |
| title_full | Complex tori Christina Birkenhake ; Herbert Lange |
| title_fullStr | Complex tori Christina Birkenhake ; Herbert Lange |
| title_full_unstemmed | Complex tori Christina Birkenhake ; Herbert Lange |
| title_short | Complex tori |
| title_sort | complex tori |
| topic | Tore (Géométrie) ram Variétés complexes ram Complex manifolds Torus (Geometry) Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Torus (DE-588)4185738-0 gnd Komplexer Torus (DE-588)4164907-2 gnd |
| topic_facet | Tore (Géométrie) Variétés complexes Complex manifolds Torus (Geometry) Komplexe Mannigfaltigkeit Torus Komplexer Torus |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008703770&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
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