LEADER 03910nam 2200685 450 001 9910465704203321 005 20200520144314.0 010 $a1-4008-3711-1 010 $a0-691-13822-2 024 7 $a10.1515/9781400837113 035 $a(CKB)2560000000081912 035 $a(EBL)1659885 035 $a(SSID)ssj0000687934 035 $a(PQKBManifestationID)11451137 035 $a(PQKBTitleCode)TC0000687934 035 $a(PQKBWorkID)10756000 035 $a(PQKB)10077485 035 $a(MiAaPQ)EBC1659885 035 $a(DE-B1597)446795 035 $a(OCoLC)979582209 035 $a(DE-B1597)9781400837113 035 $a(Au-PeEL)EBL1659885 035 $a(CaPaEBR)ebr10853262 035 $a(CaONFJC)MIL586052 035 $a(OCoLC)875819535 035 $a(EXLCZ)992560000000081912 100 $a20140412h20092009 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aClassifying spaces of degenerating polarized Hodge structures /$fKazuya Kato and Sampei Usui 205 $aCourse Book 210 1$aPrinceton, New Jersey ;$aOxfordshire, England :$cPrinceton University Press,$d2009. 210 4$dİ2009 215 $a1 online resource (349 p.) 225 1 $aAnnals of Mathematics Studies ;$vNumber 169 300 $aDescription based upon print version of record. 311 $a0-691-13821-4 320 $aIncludes bibliographical references and index. 327 $tFrontmatter -- $tContents -- $tIntroduction -- $tChapter 0. Overview -- $tChapter 1. Spaces of Nilpotent Orbits and Spaces of Nilpotent i-Orbits -- $tChapter 2. Logarithmic Hodge Structures -- $tChapter 3. Strong Topology and Logarithmic Manifolds -- $tChapter 4. Main Results -- $tChapter 5. Fundamental Diagram -- $tChapter 6. The Map ?:D#val ? DSL(2) -- $tChapter 7. Proof of Theorem A -- $tChapter 8. Proof of Theorem B -- $tChapter 9. b-Spaces -- $tChapter 10. Local Structures of DSL(2) and ?DbSL(2),?1 -- $tChapter 11. Moduli of PLH with Coefficients -- $tChapter 12. Examples and Problems -- $tAppendix -- $tReferences -- $tList of Symbols -- $tIndex 330 $aIn 1970, Phillip Griffiths envisioned that points at infinity could be added to the classifying space D of polarized Hodge structures. In this book, Kazuya Kato and Sampei Usui realize this dream by creating a logarithmic Hodge theory. They use the logarithmic structures begun by Fontaine-Illusie to revive nilpotent orbits as a logarithmic Hodge structure. The book focuses on two principal topics. First, Kato and Usui construct the fine moduli space of polarized logarithmic Hodge structures with additional structures. Even for a Hermitian symmetric domain D, the present theory is a refinement of the toroidal compactifications by Mumford et al. For general D, fine moduli spaces may have slits caused by Griffiths transversality at the boundary and be no longer locally compact. Second, Kato and Usui construct eight enlargements of D and describe their relations by a fundamental diagram, where four of these enlargements live in the Hodge theoretic area and the other four live in the algebra-group theoretic area. These two areas are connected by a continuous map given by the SL(2)-orbit theorem of Cattani-Kaplan-Schmid. This diagram is used for the construction in the first topic. 410 0$aAnnals of mathematics studies ;$vNumber 169. 606 $aHodge theory 606 $aLogarithms 608 $aElectronic books. 615 0$aHodge theory. 615 0$aLogarithms. 676 $a514/.74 686 $aSI 830$2rvk 700 $aKato$b Kazuya$g(Kazuya),$062762 702 $aUsui$b Sampei 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910465704203321 996 $aClassifying spaces of degenerating polarized Hodge structures$92488119 997 $aUNINA