
Classifying Spaces of Degenerating Polarized Hodge Structures
Princeton University Press
Will be published approx. on 7. December 2008
Book
Paperback/Softback
352 pages
978-0-691-13822-0 (ISBN)
Description
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.
Reviews / Votes
"The book ... is well and carefully written and even a beginner can learn a lot from it... It is a nice book and can be strongly recommended."--European Mathematical Society NewsletterMore details
Series
Language
English
Place of publication
New Jersey
United States
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
2 line illus.
Dimensions
Height: 234 mm
Width: 156 mm
Thickness: 19 mm
Weight
532 gr
ISBN-13
978-0-691-13822-0 (9780691138220)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions

Kazuya Kato | Sampei Usui
Classifying Spaces of Degenerating Polarized Hodge Structures
Book
12/2008
Princeton University Press
€99.04
Article exhausted; check different version

Kazuya Kato | Sampei Usui
Classifying Spaces of Degenerating Polarized Hodge Structures
E-Book
11/2008
1st Edition
Princeton University Press
€102.99
Available for download
Persons
Kazuya Kato is professor of mathematics at Kyoto University. Sampei Usui is professor of mathematics at Osaka University.
Content
*Frontmatter, pg. i*Contents, pg. vii*Introduction, pg. 1*Chapter 0. Overview, pg. 7*Chapter 1. Spaces of Nilpotent Orbits and Spaces of Nilpotent i-Orbits, pg. 70*Chapter 2. Logarithmic Hodge Structures, pg. 75*Chapter 3. Strong Topology and Logarithmic Manifolds, pg. 107*Chapter 4. Main Results, pg. 146*Chapter 5. Fundamental Diagram, pg. 157*Chapter 6. The Map psi:D#val --> DSL(2), pg. 175*Chapter 7. Proof of Theorem A, pg. 205*Chapter 8. Proof of Theorem B, pg. 226*Chapter 9. b-Spaces, pg. 244*Chapter 10. Local Structures of DSL(2) and GAMMA\DbSL(2),<=1, pg. 251*Chapter 11. Moduli of PLH with Coefficients, pg. 271*Chapter 12. Examples and Problems, pg. 277*Appendix, pg. 307*References, pg. 315*List of Symbols, pg. 321*Index, pg. 331