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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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: http://dx.doi.org/10.1090/S0002-9947-07-04161-X
PII: S 0002-9947(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.