Moduli spaces of Abelian surfaces: compactification, degenerations, and theta functions
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin u.a.
<<de>> Gruyter
1993
|
| Series: | De Gruyter expositions in mathematics
12 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 347 S. Ill. |
| ISBN: | 3110138514 |
Staff View
MARC
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| 100 | 1 | |a Hulek, Klaus |d 1952- |e Verfasser |0 (DE-588)142026077 |4 aut | |
| 245 | 1 | 0 | |a Moduli spaces of Abelian surfaces |b compactification, degenerations, and theta functions |c by Klaus Hulek ; Constantin Kahn ; Steven H. Weintraub |
| 264 | 1 | |a Berlin u.a. |b <<de>> Gruyter |c 1993 | |
| 300 | |a XII, 347 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v 12 | |
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| 650 | 7 | |a Modules, théorie des |2 ram | |
| 650 | 7 | |a Polarisation |2 jussieu | |
| 650 | 7 | |a Surface Humbert |2 jussieu | |
| 650 | 7 | |a Surface abélienne |2 jussieu | |
| 650 | 7 | |a Variétés abéliennes |2 ram | |
| 650 | 7 | |a Variëteiten van Abel |2 gtt | |
| 650 | 4 | |a Abelian varieties | |
| 650 | 4 | |a Moduli theory | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-005426802 | ||
Record in the Search Index
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| adam_text | Contents
Introduction ix
I Compactified moduli spaces 1
1 Moduli spaces 3
2 Torus embeddings and applications 14
2A Torus embeddings 14
2B Shioda and Kummer modular surfaces 20
2C The topology of Shioda and Kummer modular surfaces .... 43
3 Toroidal compactification of .4(1, p) 45
3A Boundary components 46
3B The Tits building 58
3C Toroidal compactification 65
3D Partial compactifications of A(l,p) 83
4 The boundary of A*(l,p) 125
4A Corank 2 boundary components 125
4B Transversality 147
4C The topology of A*{ ,p) 151
5 Humbert surfaces and scaffoldings 155
5A The scaffolding 155
5B Geometry of the Humbert surfaces 169
6 The Satake compactification 184
II Degenerations of abelian surfaces 191
1 Mumford s construction 195
1A Outline of the construction 195
IB Relatively complete models 196
1C Construction of G 200
ID Properties of G 202
2 The basic construction for surfaces 204
2A The basic data 204
2B Computations 207
viii Contents
3 Degenerate abelian surfaces (the principally polarized case) .... 215
3A Boundary points and Mumford s construction 215
3B Description of singular surfaces 218
3C Global aspects 230
4 Degenerate abelian surfaces (the case of (l,p) polarization) .... 235
4A Boundary points 235
4B Degenerate abelian surfaces 237
5 Polarizations on degenerate abelian surfaces 245
5A Theta functions 245
5B Extending polarizations (p = 1) 249
5C Miscellaneous remarks 257
5D The general case (p 1) 262
III The Horrocks Mumford map 271
1 The Horrocks Mumford bundle 274
1A Basic properties 274
IB Horrocks Mumford surfaces 275
1C Geometry in the space of sections 278
2 Construction of the Horrocks Mumford map 281
2A Heisenberg equivariant embeddings 281
2B Odd theta null values 289
2C Construction of the Horrocks Mumford map 292
3 Extension of the Horrocks Mumford map to *4(1, 5) 298
3A Extension to H2 298
3B Extension to Hi 300
4 Extension of the Horrocks Mumford map to *4*(1, 5) 305
4A Extension to the central boundary component 305
4B Extension to the peripheral boundary components 309
4C Extension to the corank 2 boundary components 314
Bibliography 333
Glossary of Notations 337
Index 343
|
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| author | Hulek, Klaus 1952- Kahn, Constantin P. M. Weintraub, Steven H. 1951- |
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| id | DE-604.BV008220267 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:16:35Z |
| institution | BVB |
| isbn | 3110138514 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-005426802 |
| oclc_num | 28584635 |
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| physical | XII, 347 S. Ill. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Hulek, Klaus 1952- Verfasser (DE-588)142026077 aut Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions by Klaus Hulek ; Constantin Kahn ; Steven H. Weintraub Berlin u.a. <<de>> Gruyter 1993 XII, 347 S. Ill. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 12 Espace module jussieu Modules, théorie des ram Polarisation jussieu Surface Humbert jussieu Surface abélienne jussieu Variétés abéliennes ram Variëteiten van Abel gtt Abelian varieties Moduli theory Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Modulraum (DE-588)4183462-8 s DE-604 Kahn, Constantin P. M. Verfasser aut Weintraub, Steven H. 1951- Verfasser (DE-588)113001770 aut De Gruyter expositions in mathematics 12 (DE-604)BV004069300 12 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005426802&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hulek, Klaus 1952- Kahn, Constantin P. M. Weintraub, Steven H. 1951- Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions De Gruyter expositions in mathematics Espace module jussieu Modules, théorie des ram Polarisation jussieu Surface Humbert jussieu Surface abélienne jussieu Variétés abéliennes ram Variëteiten van Abel gtt Abelian varieties Moduli theory Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Modulraum (DE-588)4183462-8 gnd |
| subject_GND | (DE-588)4140992-9 (DE-588)4183462-8 |
| title | Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions |
| title_auth | Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions |
| title_exact_search | Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions |
| title_full | Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions by Klaus Hulek ; Constantin Kahn ; Steven H. Weintraub |
| title_fullStr | Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions by Klaus Hulek ; Constantin Kahn ; Steven H. Weintraub |
| title_full_unstemmed | Moduli spaces of Abelian surfaces compactification, degenerations, and theta functions by Klaus Hulek ; Constantin Kahn ; Steven H. Weintraub |
| title_short | Moduli spaces of Abelian surfaces |
| title_sort | moduli spaces of abelian surfaces compactification degenerations and theta functions |
| title_sub | compactification, degenerations, and theta functions |
| topic | Espace module jussieu Modules, théorie des ram Polarisation jussieu Surface Humbert jussieu Surface abélienne jussieu Variétés abéliennes ram Variëteiten van Abel gtt Abelian varieties Moduli theory Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Modulraum (DE-588)4183462-8 gnd |
| topic_facet | Espace module Modules, théorie des Polarisation Surface Humbert Surface abélienne Variétés abéliennes Variëteiten van Abel Abelian varieties Moduli theory Abelsche Mannigfaltigkeit Modulraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=005426802&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV004069300 |
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