Moduli spaces of stable sheaves on schemes : restriction theorems, boundedness and the GIT construction
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Bibliographic Information
Moduli spaces of stable sheaves on schemes : restriction theorems, boundedness and the GIT construction
（MSJ memoirs, v. 33）
Mathematical Society of Japan, 2016
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science数学
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Note
Includes bibliographical references (p. 153)
Description and Table of Contents
Description
The notion of stability for algebraic vector bundles on curves was originally introduced by Mumford, and moduli spaces of semi-stable vector bundles were studied intensively by Indian mathematicians. The notion of stability for algebraic sheaves was generalized to higher dimensional varieties. The study of moduli spaces of algebraic sheaves not only on curves but also on higher dimensional algebraic varieties has attracted much interest for decades and its importance has been increasing not only in algebraic geometry but also in related fields as differential geometry, mathematical physics.Masaki Maruyama is one of the pioneers in the theory of algebraic vector bundles on higher dimensional algebraic varieties. This book is a posthumous publication of his manuscript. It starts with basic concepts such as stability of sheaves, Harder-Narasimhan filtration and generalities on boundedness of sheaves. It then presents fundamental theorems on semi-stable sheaves: restriction theorems of semi-stable sheaves, boundedness of semi-stable sheaves, tensor products of semi-stable sheaves. Finally, after constructing quote-schemes, it explains the construction of the moduli space of semi-stable sheaves. The theorems are stated in a general setting and the proofs are rigorous.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets
Table of Contents
- Stable Sheaves
- Restriction Theorems and Boundedness
- Construction of Moduli Spaces
- Appendices: On Langer's Work
- Some Properties of the Moduli
- Bibliography
- Glossary of Notations
by "Nielsen BookData"