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Record Nr. |
UNINA9910809577303321 |
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Autore |
Kato Kazuya (Kazuya) |
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Titolo |
Classifying spaces of degenerating polarized Hodge structures / / Kazuya Kato and Sampei Usui |
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Pubbl/distr/stampa |
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Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2009 |
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©2009 |
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ISBN |
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1-4008-3711-1 |
0-691-13822-2 |
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Edizione |
[Course Book] |
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Descrizione fisica |
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1 online resource (349 p.) |
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Collana |
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Annals of Mathematics Studies ; ; Number 169 |
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Classificazione |
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Disciplina |
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Soggetti |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di bibliografia |
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Includes bibliographical references and index. |
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Nota di contenuto |
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Frontmatter -- Contents -- Introduction -- Chapter 0. Overview -- Chapter 1. Spaces of Nilpotent Orbits and Spaces of Nilpotent i-Orbits -- Chapter 2. Logarithmic Hodge Structures -- Chapter 3. Strong Topology and Logarithmic Manifolds -- Chapter 4. Main Results -- Chapter 5. Fundamental Diagram -- Chapter 6. The Map ψ:D#val → DSL(2) -- Chapter 7. Proof of Theorem A -- Chapter 8. Proof of Theorem B -- Chapter 9. b-Spaces -- Chapter 10. Local Structures of DSL(2) and ΓDbSL(2),≤1 -- Chapter 11. Moduli of PLH with Coefficients -- Chapter 12. Examples and Problems -- Appendix -- References -- List of Symbols -- Index |
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Sommario/riassunto |
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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 |
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