Classifying spaces of degenerating polarized hodge structures

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Hauptverfasser: Kato, Kazuya 1952- (VerfasserIn), Usui, Sampei (VerfasserIn)
Format: Buch
Sprache:English
Veröffentlicht: Princeton, NJ Princeton Univ. Press 2009
Schriftenreihe:Annals of mathematics studies 169
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Datensatz im Suchindex

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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
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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
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