03910nam 2200685 450 991046570420332120200520144314.01-4008-3711-10-691-13822-210.1515/9781400837113(CKB)2560000000081912(EBL)1659885(SSID)ssj0000687934(PQKBManifestationID)11451137(PQKBTitleCode)TC0000687934(PQKBWorkID)10756000(PQKB)10077485(MiAaPQ)EBC1659885(DE-B1597)446795(OCoLC)979582209(DE-B1597)9781400837113(Au-PeEL)EBL1659885(CaPaEBR)ebr10853262(CaONFJC)MIL586052(OCoLC)875819535(EXLCZ)99256000000008191220140412h20092009 uy 0engur|n|---|||||txtccrClassifying spaces of degenerating polarized Hodge structures /Kazuya Kato and Sampei UsuiCourse BookPrinceton, New Jersey ;Oxfordshire, England :Princeton University Press,2009.©20091 online resource (349 p.)Annals of Mathematics Studies ;Number 169Description based upon print version of record.0-691-13821-4 Includes bibliographical references and index.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 -- IndexIn 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.Annals of mathematics studies ;Number 169.Hodge theoryLogarithmsElectronic books.Hodge theory.Logarithms.514/.74SI 830rvkKato Kazuya(Kazuya),62762Usui SampeiMiAaPQMiAaPQMiAaPQBOOK9910465704203321Classifying spaces of degenerating polarized Hodge structures2488119UNINA02064nam 2200553 450 991045943100332120200520144314.01-282-89238-X97866128923871-4094-1508-2(CKB)2670000000055181(EBL)4439715(OCoLC)950904813(SSID)ssj0000475221(PQKBManifestationID)11913319(PQKBTitleCode)TC0000475221(PQKBWorkID)10463433(PQKB)11654341(MiAaPQ)EBC4439715(Au-PeEL)EBL4439715(CaPaEBR)ebr10428165(CaONFJC)MIL289238(EXLCZ)99267000000005518120160416h20102010 uy 0engur|n|---|||||txtccrThe discovery of the large, rich, and beautiful empire of guiana /Sir W. RaleghSurrey, England ;Burlington, Vermont :Ashgate Publishing Limited :Ashgate Publishing Company,2010.©20101 online resource (333 p.)Hakluyt Society, First Series ;v.3Includes index.1-4094-1269-5 COVER; THE EPISTLE; TO THE READER; EDITOR'S PREFACE; INTRODUCTION; THE DISCOVERIE OF GUIANA; ADVERTISEMENT TO THE READER; LETTERS TAKEN AT SEA BY CAPTAINE GEORGE POPHAM 1594; APPENDIX; OF THE VOYAGE FOR GUIANA; SIR WALTER RALEGH'S JOURNAL OF HIS SECOND VOYAGE TO GUIANA; ERRATA; INDEX; A; B; C; P; E; F; G; H; I; J; K; L; M; N; O; P; Q; R; S; T; U; V; W; Y; MAP: TO ILLUSTRATE SIR WALTER RALEGH'S VOYAGEHakluyt Society, First SeriesGuianaDiscovery and explorationElectronic books.942.0550924Ralegh W.931803MiAaPQMiAaPQMiAaPQBOOK9910459431003321The discovery of the large, rich, and beautiful empire of guiana2095994UNINA