Classifying spaces of degenerating polarized Hodge structures / / Kazuya Kato and Sampei Usui

• Autore: Kato Kazuya (Kazuya)
• Pubblicazione: Princeton, New Jersey ; ; Oxfordshire, England : , : Princeton University Press, , 2009; ©2009
• Edizione: Course Book
• Descrizione fisica: 1 online resource (349 p.)
• Disciplina: 514/.74
• Soggetto topico: Hodge theory; Logarithms
• Soggetto non controllato: Algebraic group; Algebraic variety; Analytic manifold; Analytic space; Annulus (mathematics); Arithmetic group; Atlas (topology); Canonical map; Classifying space; Coefficient; Cohomology; Compactification (mathematics); Complex manifold; Complex number; Congruence subgroup; Conjecture; Connected component (graph theory); Continuous function; Convex cone; Degeneracy (mathematics); Diagram (category theory); Differential form; Direct image functor; Divisor; Elliptic curve; Equivalence class; Existential quantification; Finite set; Functor; Geometry; Hodge structure; Hodge theory; Homeomorphism; Homomorphism; Inverse function; Iwasawa decomposition; Local homeomorphism; Local ring; Local system; Logarithmic; Maximal compact subgroup; Modular curve; Modular form; Moduli space; Monodromy; Monoid; Morphism; Natural number; Nilpotent orbit; Nilpotent; Open problem; Open set; P-adic Hodge theory; P-adic number; Point at infinity; Proper morphism; Pullback (category theory); Quotient space (topology); Rational number; Relative interior; Ring (mathematics); Ring homomorphism; Scientific notation; Set (mathematics); Sheaf (mathematics); Smooth morphism; Special case; Strong topology; Subgroup; Subobject; Subset; Surjective function; Tangent bundle; Taylor series; Theorem; Topological space; Topology; Transversality (mathematics); Two-dimensional space; Vector bundle; Vector space; Weak topology
• Classificazione: SI 830
• Persona (resp. second.): UsuiSampei
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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
• Sommario/riassunto: 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.
• Titolo autorizzato: Classifying spaces of degenerating polarized Hodge structures
• ISBN: 1-4008-3711-1; 0-691-13822-2
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910791746503321
• Lo trovi qui: Univ. Federico II
• Serie: Annals of mathematics studies ; ; Number 169.