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Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169).
In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2008.
|
| Colección: | Annals of mathematics studies ;
no. 169. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 003 | OCoLC | ||
| 005 | 20231005004200.0 | ||
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| 100 | 1 | |a Kato, K. |q (Kazuya) | |
| 245 | 1 | 0 | |a Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169). |
| 260 | |a Princeton : |b Princeton University Press, |c 2008. | ||
| 300 | |a 1 online resource (349 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 490 | 1 | |a Annals of Mathematics Studies ; |v number 169 | |
| 588 | 0 | |a Print version record. | |
| 520 | |a In 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic. | ||
| 546 | |a In English. | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 650 | 0 | |a Hodge theory. | |
| 650 | 0 | |a Logarithms. | |
| 650 | 4 | |a Mathematics. | |
| 650 | 4 | |a Physical Sciences & Mathematics. | |
| 650 | 4 | |a Geometry. | |
| 650 | 6 | |a Théorie de Hodge. | |
| 650 | 6 | |a Logarithmes. | |
| 650 | 7 | |a logarithms. |2 aat | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Linear. |2 bisacsh | |
| 650 | 7 | |a Hodge theory |2 fast | |
| 650 | 7 | |a Logarithms |2 fast | |
| 700 | 1 | |a Usui, Sampei. | |
| 776 | 0 | 8 | |i Print version: |a Kato, Kazuya. |t Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169). |d Princeton : Princeton University Press, ©2008 |z 9780691138220 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 169. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt6wpzkw |z Texto completo |
| 880 | 0 | |6 505-00/(N |a Cover; Title; Copyright; Contents; Introduction; Chapter 0. Overview; 0.1 Hodge Theory; 0.2 Logarithmic Hodge Theory; 0.3 Griffiths Domains and Moduli of PH; 0.4 Toroidal Partial Compactifications of Г\D and Moduli of PLH; 0.5 Fundamental Diagram and Other Enlargements of D; 0.6 Plan of This Book; 0.7 Notation and Convention; Chapter 1. Spaces of Nilpotent Orbits and Spaces of Nilpotent i-Orbits; 1.1 Hodge Structures and Polarized Hodge Structures; 1.2 Classifying Spaces of Hodge Structures; 1.3 Extended Classifying Spaces; Chapter 2. Logarithmic Hodge Structures; 2.1 Logarithmic Structures. | |
| 880 | 8 | |6 505-00/(S |a 2.2 Ringed Spaces (X^log, O^log X)2.3 Local Systems on X^log; 2.4 Polarized Logarithmic Hodge Structures; 2.5 Nilpotent Orbits and Period Maps; 2.6 Logarithmic Mixed Hodge Structures; Chapter 3. Strong Topology and Logarithmic Manifolds; 3.1 Strong Topology; 3.2 Generalizations of Analytic Spaces; 3.3 Sets Eσ and E^♯σ; 3.4 Spaces Eσ, Г\DΣ, E^♯σ, and D^♯Σ; 3.5 Infinitesimal Calculus and Logarithmic Manifolds; 3.6 Logarithmic Modifications; Chapter 4. Main Results; 4.1 Theorem A: The Spaces Eσ, Г\DΣ and Г\DΣ♯; 4.2 Theorem B: The Functor PLНФ; 4.3 Extensions of Period Maps. | |
| 880 | 8 | |6 505-00/(S |a 4.4 Infinitesimal Period MapsChapter 5. Fundamental Diagram; 5.1 Borel-Serre Spaces (Review); 5.2 Spaces of SL(2)-Orbits (Review); 5.3 Spaces of Valuative Nilpotent Orbits; 5.4 Valuative Nilpotent i-Orbits and SL(2)-Orbits; Chapter 6. The Map ψ : D^♯val → DSL(2); 6.1 Review of [CKS] and Some Related Results; 6.2 Proof of Theorem 5.4.2; 6.3 Proof of Theorem 5.4.3 (i); 6.4 Proofs of Theorem 5.4.3 (ii) and Theorem 5.4.4; Chapter 7. Proof of Theorem A; 7.1 Proof of Theorem A (i); 7.2 Action of σC on Eσ; 7.3 Proof of Theorem A for Г(σ)^gp\Dσ; 7.4 Proof of Theorem A for Г\DΣ. | |
| 880 | 8 | |6 505-00/(N |a Chapter 8. Proof of Theorem B8.1 Logarithmic Local Systems; 8.2 Proof of Theorem B; 8.3 Relationship among Categories of Generalized Analytic Spaces; 8.4 Proof of Theorem 0.5.29; Chapter 9. ♭-Spaces; 9.1 Definitions and Main Properties; 9.2 Proofs of Theorem 9.1.4 for Г\X^♭BS, Г\D^♭BS, and Г\D^♭BS, val; 9.3 Proof of Theorem 9.1.4 for Г\D^♭SL(2), ≤1; 9.4 Extended Period Maps; Chapter 10. Local Structures of DSL(2) and Г\D^♭SL(2), ≤1; 10.1 Local Structures of DSL(2); 10.2 A Special Open Neighborhood U(p); 10.3 Proof of Theorem 10.1.3; 10.4 Local Structures of DSL(2), ≤1 and Г\D^♭SL(2), ≤1. | |
| 880 | 8 | |6 505-00/(N |a Chapter 11. Moduli of PLH with Coefficients11.1 Space Г\ D^AΣ; 11.2 PLH with Coefficients; 11.3 Moduli; Chapter 12. Examples and Problems; 12.1 Siegel Upper Half Spaces; 12.2 Case GR ≃ O(1, n − 1, R); 12.3 Example of Weight 3 (A); 12.4 Example of Weight 3 (B); 12.5 Relationship with [U2]; 12.6 Complete Fans; 12.7 Problems; Appendix; A1 Positive Direction of Local Monodromy; A2 Proper Base Change Theorem for Topological Spaces; References; List of Symbols; Index. | |
| 938 | |a ProQuest Ebook Central |b EBLB |n EBL1659885 | ||
| 938 | |a YBP Library Services |b YANK |n 11704261 | ||
| 994 | |a 92 |b IZTAP | ||