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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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The elementary transformation of vector bundles on regular schemes
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by Takuro Abe PDF
Trans. Amer. Math. Soc. 359 (2007), 4285-4295 Request permission

Abstract:

We give a generalized definition of an elementary transformation of vector bundles on regular schemes by using Maximal Cohen-Macaulay sheaves on divisors. This definition is a natural extension of that given by Maruyama, and has a connection with that given by Sumihiro. By this elementary transformation, we can construct, up to tensoring line bundles, all vector bundles from trivial bundles on nonsingular quasi-projective varieties over an algebraically closed field. Moreover, we give an application of this theory to reflexive sheaves.
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Additional Information
  • Takuro Abe
  • Affiliation: Department of Mathematics, Graduate School of Science, Kyoto University, Kyoto, 606-8502, Japan
  • Address at time of publication: Department of Mathematics, Hokkaido University, Kita-10, Nishi-8, Kita-Ku, Sapporo, Hokkaido, 060-0810, Japan
  • Email: abetaku@kusm.kyoto-u.ac.jp, abetaku@math.sci.hokudai.ac.jp
  • Received by editor(s): July 16, 2004
  • Received by editor(s) in revised form: July 23, 2005
  • Published electronically: March 20, 2007
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 359 (2007), 4285-4295
  • MSC (2000): Primary 14F05
  • DOI: https://doi.org/10.1090/S0002-9947-07-04161-X
  • MathSciNet review: 2309185