Classifying spaces of degenerating polarized hodge structures:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Princeton, NJ
Princeton Univ. Press
2009
|
| Series: | Annals of mathematics studies
169 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 336 S. |
| ISBN: | 9780691138213 9780691138220 0691138222 |
Staff View
MARC
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| 245 | 1 | 0 | |a Classifying spaces of degenerating polarized hodge structures |c Kazuya Kato ; Sampei Usui |
| 264 | 1 | |a Princeton, NJ |b Princeton Univ. Press |c 2009 | |
| 300 | |a IX, 336 S. | ||
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Record in the Search Index
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| adam_text | Contents
Introduction 1
Chapter 0. Overview 7
0.1 Hodge Theory 7
0.2 Logarithmic Hodge Theory 11
0.3 Griffiths Domains and Moduli of PH 24
0.4 Toroidal Partial Compactifications of V D and Moduli of PLH 30
0.5 Fundamental Diagram and Other Enlargements of D 43
0.6 Plan of This Book 66
0.7 Notation and Convention 67
Chapter 1. Spaces of Nilpotent Orbits and Spaces of Nilpotent /-Orbits 70
1.1 Hodge Structures and Polarized Hodge Structures 70
1.2 Classifying Spaces of Hodge Structures 71
1.3 Extended Classifying Spaces 72
Chapter 2. Logarithmic Hodge Structures 75
2.1 Logarithmic Structures 75
2.2 Ringed Spaces (Xlo«, £ £g) 81
2.3 Local Systems on Xlog 88
2.4 Polarized Logarithmic Hodge Structures 94
2.5 Nilpotent Orbits and Period Maps 97
2.6 Logarithmic Mixed Hodge Structures 105
Chapter 3. Strong Topology and Logarithmic Manifolds 107
3.1 Strong Topology 107
3.2 Generalizations of Analytic Spaces 115
3.3 Sets Ea and E^ 120
3.4 Spaces Ea. r Z i;. E%, and D% 125
3.5 Infinitesimal Calculus and Logarithmic Manifolds 127
3.6 Logarithmic Modifications 133
Chapter 4. Main Results 146
4.1 Theorem A: The Spaces En, r Dj:, and r D^ 146
4.2 Theorem B: The Functor PLH j, 147
4.3 Extensions of Period Maps 148
4.4 Infinitesimal Period Maps 153
viii CONTENTS
Chapter 5. Fundamental Diagram 157
5.1 Borel-Serre Spaces (Review) 158
5.2 Spaces of SL(2)-Orbits (Review) 165
5.3 Spaces of Vaiuative Nilpotent Orbits 170
5.4 Valuative Nilpotent /-Orbits and SL(2)-Orbits 173
Chapter 6. The Map f : D;al -» DSL(2) 175
6.1 Review of [CKS] and Some Related Results 175
6.2 Proof of Theorem 5.4.2 186
6.3 Proof of Theorem 5.4.3 (i) 190
6.4 Proofs of Theorem 5.4.3 (ii) and Theorem 5.4.4 195
Chapter 7. Proof of Theorem A 205
7.1 Proof of Theorem A (i) 205
7.2 Action of ac on Ea 209
7.3 ProofofTheoremAforrVpXD,, 215
7.4 Proof of Theorem A for T DE 220
Chapter 8. Proof of Theorem B 226
8.1 Logarithmic Local Systems 226
8.2 Proof of Theorem B 229
8.3 Relationship among Categories of Generalized
Analytic Spaces 235
8.4 Proof of Theorem 0.5.29 241
Chapter 9. b-Spaces 244
9.1 Definitions and Main Properties 244
9.2 Proofs of Theorem 9.1.4 for r X^s, r D^s, and r / ^val 246
9.3 ProofofTheorem 9.1.4for r / s,(2) 1 248
9.4 Extended Period Maps ~ 249
Chapter 10. Local Structures of Z sl 2) and r DSL(D i 251
10.1 Local Structures of £ SL(2) 251
10.2 A Special Open Neighborhood U(p) 255
10.3 Proof of Theorem 10.1.3 263
10.4 Local Structures of Osl(2). i and r Z s,(2) ] 269
Chapter 11. Moduli of PLH with Coefficients 271
11.1 Space r /)£ 271
11.2 PLH with Coefficients 274
11.3 Moduli 275
Chapter 12. Examples and Problems 277
12.1 SiegelUpper Half Spaces 277
12.2 Case GR~O(l.n- 1,R) 281
12.3 ExatnpleofWeight3(A 290
12.4 Example of Weight 3 (B) 295
CONTENTS ix
12.5 Relationship with [U2] 299
12.6 Complete Fans 301
12.7 Problems 304
Appendix 307
Al Positive Direction of Local Monodromy 307
A2 Proper Base Change Theorem for Topological Spaces 310
References 315
List of Symbols 321
Index 331
|
| any_adam_object | 1 |
| author | Kato, Kazuya 1952- Usui, Sampei |
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| dewey-full | 514/.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.74 |
| dewey-search | 514/.74 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV035273212 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T21:30:09Z |
| institution | BVB |
| isbn | 9780691138213 9780691138220 0691138222 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017078542 |
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| physical | IX, 336 S. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | Princeton Univ. Press |
| record_format | marc |
| series | Annals of mathematics studies |
| series2 | Annals of mathematics studies |
| spelling | Kato, Kazuya 1952- Verfasser (DE-588)113479778 aut Classifying spaces of degenerating polarized hodge structures Kazuya Kato ; Sampei Usui Princeton, NJ Princeton Univ. Press 2009 IX, 336 S. txt rdacontent n rdamedia nc rdacarrier Annals of mathematics studies 169 Hodge theory Logarithms Hodge-Struktur (DE-588)4406134-1 gnd rswk-swf Logarithmus (DE-588)4168047-9 gnd rswk-swf Hodge-Theorie (DE-588)4135967-7 gnd rswk-swf Hodge-Struktur (DE-588)4406134-1 s DE-604 Hodge-Theorie (DE-588)4135967-7 s Logarithmus (DE-588)4168047-9 s Usui, Sampei Verfasser (DE-588)137803354 aut Annals of mathematics studies 169 (DE-604)BV000000991 169 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017078542&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Kato, Kazuya 1952- Usui, Sampei Classifying spaces of degenerating polarized hodge structures Annals of mathematics studies Hodge theory Logarithms Hodge-Struktur (DE-588)4406134-1 gnd Logarithmus (DE-588)4168047-9 gnd Hodge-Theorie (DE-588)4135967-7 gnd |
| subject_GND | (DE-588)4406134-1 (DE-588)4168047-9 (DE-588)4135967-7 |
| title | Classifying spaces of degenerating polarized hodge structures |
| title_auth | Classifying spaces of degenerating polarized hodge structures |
| title_exact_search | Classifying spaces of degenerating polarized hodge structures |
| title_full | Classifying spaces of degenerating polarized hodge structures Kazuya Kato ; Sampei Usui |
| title_fullStr | Classifying spaces of degenerating polarized hodge structures Kazuya Kato ; Sampei Usui |
| title_full_unstemmed | Classifying spaces of degenerating polarized hodge structures Kazuya Kato ; Sampei Usui |
| title_short | Classifying spaces of degenerating polarized hodge structures |
| title_sort | classifying spaces of degenerating polarized hodge structures |
| topic | Hodge theory Logarithms Hodge-Struktur (DE-588)4406134-1 gnd Logarithmus (DE-588)4168047-9 gnd Hodge-Theorie (DE-588)4135967-7 gnd |
| topic_facet | Hodge theory Logarithms Hodge-Struktur Logarithmus Hodge-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017078542&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000991 |
| work_keys_str_mv | AT katokazuya classifyingspacesofdegeneratingpolarizedhodgestructures AT usuisampei classifyingspacesofdegeneratingpolarizedhodgestructures |