Complex tori:
"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...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1999
|
| Schriftenreihe: | Progress in mathematics
177 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | "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."--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 |
| Beschreibung: | 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_ | 1804127469119209472 |
|---|---|
| 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
|
| any_adam_object | 1 |
| author | Birkenhake, Christina Lange, Herbert |
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| dewey-full | 514/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.3 |
| dewey-search | 514/.3 |
| dewey-sort | 3514 13 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012798654 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:33:50Z |
| institution | BVB |
| isbn | 3764341033 0817641033 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008703770 |
| oclc_num | 41404664 |
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| physical | XV, 251 S. |
| publishDate | 1999 |
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| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Birkenhake, Christina Verfasser (DE-588)141526335 aut Complex tori Christina Birkenhake ; Herbert Lange Boston [u.a.] Birkhäuser 1999 XV, 251 S. txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 177 "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."--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 Tore (Géométrie) ram Variétés complexes ram Complex manifolds Torus (Geometry) Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Torus (DE-588)4185738-0 gnd rswk-swf Komplexer Torus (DE-588)4164907-2 gnd rswk-swf Komplexer Torus (DE-588)4164907-2 s DE-604 Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Torus (DE-588)4185738-0 s Lange, Herbert Verfasser aut Progress in mathematics 177 (DE-604)BV000004120 177 HBZ Datenaustausch application/pdf 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 Inhaltsverzeichnis |
| 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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