TY - BOOK UR - http://lib.ugent.be/catalog/ebk01:2560000000081912 ID - ebk01:2560000000081912 ET - Course Book. LA - eng TI - Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) PY - 2009 SN - 9781400837113 AU - Kato, Kazuya, author. AU - Usui, Sampei, author. AB - 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. ER -Download RIS file
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007 | cr |n||||||||n | ||
008 | 151027s2009||||||||||||o|||||||||||eng|| | ||
020 | a 9781400837113 | ||
024 | 7 | a 10.1515/9781400837113 2 doi | |
035 | a (DE-B1597)446795 | ||
035 | a (OCoLC)761158505 | ||
035 | a (OCoLC)875819535 | ||
040 | a IN-ChSCO b eng c IN-ChSCO e rda | ||
041 | a eng | ||
050 | 4 | a QA564 .K364 2008 | |
050 | 4 | a QA564 b .K364 2009 | |
072 | 7 | a MAT x 002050 2 bisacsh | |
072 | 7 | a MAT002050 2 bisacsh | |
082 | 4 | a 514.74 2 23 | |
082 | 4 | a 514/.74 2 22 | |
100 | 1 | a Kato, Kazuya, e author. | |
245 | 1 | a Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / c Kazuya Kato, Sampei Usui. | |
250 | a Course Book. | ||
264 | 1 | a Princeton, N.J. : b Princeton University Press, c [2009]. | |
264 | 4 | c ©2009. | |
300 | a 1 online resource (352 pages) : b illustrations. | ||
336 | a text 2 rdacontent | ||
337 | a computer 2 rdamedia | ||
338 | a online resource 2 rdacarrier | ||
347 | a text file b PDF 2 rda | ||
490 | a Annals of Mathematics Studies, x 0066-2313 ; v 169 | ||
505 | t Frontmatter -- t Contents -- t Introduction -- t Chapter 0. Overview -- t Chapter 1. Spaces of Nilpotent Orbits and Spaces of Nilpotent i-Orbits -- t Chapter 2. Logarithmic Hodge Structures -- t Chapter 3. Strong Topology and Logarithmic Manifolds -- t Chapter 4. Main Results -- t Chapter 5. Fundamental Diagram -- t Chapter 6. The Map ψ:D -- t Chapter 7. Proof of Theorem A -- t Chapter 8. Proof of Theorem B -- t Chapter 9. b-Spaces -- t Chapter 10. Local Structures of D -- t Chapter 11. Moduli of PLH with Coefficients -- t Chapter 12. Examples and Problems -- t Appendix -- t References -- t List of Symbols -- t Index. | ||
520 | a 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. | ||
533 | a Electronic reproduction. b Princeton, N.J. : c Princeton University Press, d 2009. n Mode of access: World Wide Web. n System requirements: Web browser. n Access may be restricted to users at subscribing institutions. | ||
538 | a Mode of access: Internet via World Wide Web. | ||
546 | a In English. | ||
588 | a Description based on online resource; title from PDF title page (publisher’s Web site, viewed October 27 2015) | ||
650 | a Hodge theory. | ||
650 | a Logarithms. | ||
650 | a MATHEMATICS v Algebra v Linear. | ||
650 | 4 | a Algebra and Number Theory. | |
650 | 4 | a Hodge theory. | |
650 | 4 | a Logarithms. | |
650 | 4 | a Mathematics. | |
650 | 4 | a Mathematik. | |
700 | 1 | a Usui, Sampei, e author. | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Annals of Mathematics Backlist eBook Package z 978-3-11-049491-4 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2013 z 978-3-11-044250-2 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton eBook Package Backlist 2000-2014 z 978-3-11-045953-1 | |
773 | 8 | i Title is part of eBook package: d De Gruyter t Princeton Univ. Press eBook Package 2000-2013 z 978-3-11-041343-4 | |
830 | a Annals of Mathematics Studies ; v 169. | ||
856 | 4 | u https://doi.org/10.1515/9781400837113 | |
856 | 4 | 2 | 3 Cover u https://www.degruyter.com/doc/cover/9781400837113.jpg |
912 | a 978-3-11-041343-4 Princeton Univ. Press eBook Package 2000-2013 | ||
912 | a 978-3-11-044250-2 Princeton eBook Package Backlist 2000-2013 | ||
912 | a 978-3-11-045953-1 Princeton eBook Package Backlist 2000-2014 | ||
912 | a 978-3-11-049491-4 Princeton Annals of Mathematics Backlist eBook Package | ||
912 | a GBV-deGruyter-alles | ||
912 | a GBV-deGruyter-PDA12STME | ||
912 | a GBV-deGruyter-PDA13ENGE | ||
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