Moduli spaces of stable sheaves on schemes : restriction theorems, boundedness and the GIT construction


Moduli spaces of stable sheaves on schemes : restriction theorems, boundedness and the GIT construction

Masaki Maruyama ; with collaboration of T. Abe and M. Inaba

(MSJ memoirs, v. 33)

Mathematical Society of Japan, 2016

  • : [pbk.]

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Includes bibliographical references (p. 153)



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


  • Stable Sheaves
  • Restriction Theorems and Boundedness
  • Construction of Moduli Spaces
  • Appendices: On Langer's Work
  • Some Properties of the Moduli
  • Bibliography
  • Glossary of Notations

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  • ISBN
    • 9784864970341
  • 出版国コード
  • タイトル言語コード
  • 本文言語コード
  • 出版地
  • ページ数/冊数
    xi, 154 p.
  • 大きさ
    25 cm
  • 親書誌ID