Classifying Spaces of Degenerating Polarized Hodge Structures 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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2009-2 出版日期

352 页数

$ 96.05 价格

Annals of Mathematics Studies 丛书系列

9780691138213 图书编码

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Classifying Spaces of Degenerating Polarized Hodge Structures 在线电子书 epub 下载 mobi 下载 pdf 下载 txt 下载 2024

Classifying Spaces of Degenerating Polarized Hodge Structures 在线电子书 pdf 下载 txt下载 epub 下载 mobi 下载 2024

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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.

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