The elementary transformation of vector bundles on regular schemes

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

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Sheaves
Vector Bundle
Cohen-Macaulay
Projective Variety
Line Bundle
Natural Extension
Algebraically closed
Divisor
Bundle
Trivial

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

The elementary transformation of vector bundles on regular schemes. / Abe, Takuro.

In: Transactions of the American Mathematical Society, Vol. 359, No. 9, 01.12.2007, p. 4285-4295.

Research output: Contribution to journalArticle

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