The elementary transformation of vector bundles on regular schemes

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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.

Original languageEnglish
Pages (from-to)4285-4295
Number of pages11
JournalTransactions of the American Mathematical Society
Volume359
Issue number9
DOIs
Publication statusPublished - Dec 1 2007
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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