The elementary transformation of vector bundles on regular schemes

Author:
Takuro Abe

Journal:
Trans. Amer. Math. Soc. **359** (2007), 4285-4295

MSC (2000):
Primary 14F05

DOI:
https://doi.org/10.1090/S0002-9947-07-04161-X

Published electronically:
March 20, 2007

MathSciNet review:
2309185

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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.

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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

DOI:
https://doi.org/10.1090/S0002-9947-07-04161-X

Received by editor(s):
July 16, 2004

Received by editor(s) in revised form:
July 23, 2005

Published electronically:
March 20, 2007

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.