Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / / Sampei Usui, Kazuya Kato.
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...
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Kato, Kazuya, author. aut http://id.loc.gov/vocabulary/relators/aut Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / Sampei Usui, Kazuya Kato. Course Book Princeton, NJ : Princeton University Press, [2008] ©2009 1 online resource (352 p.) : 2 line illus. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of Mathematics Studies ; 169 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 restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star 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. Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) Hodge theory. Logarithms. MATHEMATICS Algebra Linear. MATHEMATICS / Algebra / Linear. bisacsh 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. 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. Usui, Sampei, author. aut http://id.loc.gov/vocabulary/relators/aut Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 9783110494914 ZDB-23-PMB Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 9783110442502 print 9780691138220 https://doi.org/10.1515/9781400837113 https://www.degruyter.com/isbn/9781400837113 Cover https://www.degruyter.com/document/cover/isbn/9781400837113/original |
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English |
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Kato, Kazuya, Kato, Kazuya, Usui, Sampei, |
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Kato, Kazuya, Kato, Kazuya, Usui, Sampei, Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / Annals of Mathematics Studies ; 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 |
author_facet |
Kato, Kazuya, Kato, Kazuya, Usui, Sampei, Usui, Sampei, Usui, Sampei, |
author_variant |
k k kk k k kk s u su |
author_role |
VerfasserIn VerfasserIn VerfasserIn |
author2 |
Usui, Sampei, Usui, Sampei, |
author2_variant |
s u su |
author2_role |
VerfasserIn VerfasserIn |
author_sort |
Kato, Kazuya, |
title |
Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / |
title_full |
Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / Sampei Usui, Kazuya Kato. |
title_fullStr |
Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / Sampei Usui, Kazuya Kato. |
title_full_unstemmed |
Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / Sampei Usui, Kazuya Kato. |
title_auth |
Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / |
title_alt |
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 |
title_new |
Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / |
title_sort |
classifying spaces of degenerating polarized hodge structures. (am-169) / |
series |
Annals of Mathematics Studies ; |
series2 |
Annals of Mathematics Studies ; |
publisher |
Princeton University Press, |
publishDate |
2008 |
physical |
1 online resource (352 p.) : 2 line illus. Issued also in print. |
edition |
Course Book |
contents |
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 |
isbn |
9781400837113 9783110494914 9783110442502 9780691138220 |
callnumber-first |
Q - Science |
callnumber-subject |
QA - Mathematics |
callnumber-label |
QA564 |
callnumber-sort |
QA 3564 K364 42009 |
genre_facet |
Algebra Linear. |
url |
https://doi.org/10.1515/9781400837113 https://www.degruyter.com/isbn/9781400837113 https://www.degruyter.com/document/cover/isbn/9781400837113/original |
illustrated |
Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
514 - Topology |
dewey-full |
514/.74 |
dewey-sort |
3514 274 |
dewey-raw |
514/.74 |
dewey-search |
514/.74 |
doi_str_mv |
10.1515/9781400837113 |
oclc_num |
979582209 |
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Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020 Title is part of eBook package: De Gruyter Princeton University Press eBook-Package Backlist 2000-2013 |
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Classifying Spaces of Degenerating Polarized Hodge Structures. (AM-169) / |
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