LEADER 06597nam  2201657   450 
001 9910791746503321
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(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(MiAaPQ)EBC1659885
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
610   $aAlgebraic group.
610   $aAlgebraic variety.
610   $aAnalytic manifold.
610   $aAnalytic space.
610   $aAnnulus (mathematics).
610   $aArithmetic group.
610   $aAtlas (topology).
610   $aCanonical map.
610   $aClassifying space.
610   $aCoefficient.
610   $aCohomology.
610   $aCompactification (mathematics).
610   $aComplex manifold.
610   $aComplex number.
610   $aCongruence subgroup.
610   $aConjecture.
610   $aConnected component (graph theory).
610   $aContinuous function.
610   $aConvex cone.
610   $aDegeneracy (mathematics).
610   $aDiagram (category theory).
610   $aDifferential form.
610   $aDirect image functor.
610   $aDivisor.
610   $aElliptic curve.
610   $aEquivalence class.
610   $aExistential quantification.
610   $aFinite set.
610   $aFunctor.
610   $aGeometry.
610   $aHodge structure.
610   $aHodge theory.
610   $aHomeomorphism.
610   $aHomomorphism.
610   $aInverse function.
610   $aIwasawa decomposition.
610   $aLocal homeomorphism.
610   $aLocal ring.
610   $aLocal system.
610   $aLogarithmic.
610   $aMaximal compact subgroup.
610   $aModular curve.
610   $aModular form.
610   $aModuli space.
610   $aMonodromy.
610   $aMonoid.
610   $aMorphism.
610   $aNatural number.
610   $aNilpotent orbit.
610   $aNilpotent.
610   $aOpen problem.
610   $aOpen set.
610   $aP-adic Hodge theory.
610   $aP-adic number.
610   $aPoint at infinity.
610   $aProper morphism.
610   $aPullback (category theory).
610   $aQuotient space (topology).
610   $aRational number.
610   $aRelative interior.
610   $aRing (mathematics).
610   $aRing homomorphism.
610   $aScientific notation.
610   $aSet (mathematics).
610   $aSheaf (mathematics).
610   $aSmooth morphism.
610   $aSpecial case.
610   $aStrong topology.
610   $aSubgroup.
610   $aSubobject.
610   $aSubset.
610   $aSurjective function.
610   $aTangent bundle.
610   $aTaylor series.
610   $aTheorem.
610   $aTopological space.
610   $aTopology.
610   $aTransversality (mathematics).
610   $aTwo-dimensional space.
610   $aVector bundle.
610   $aVector space.
610   $aWeak topology.
615  0$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   $a9910791746503321
996   $aClassifying spaces of degenerating polarized Hodge structures$93694341
997   $aUNINA