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# The Elementary Transformation of Vector Bundles on Regular Schemes

@inproceedings{Abe2007TheET, title={The Elementary Transformation of Vector Bundles on Regular Schemes}, author={Takuro Abe}, year={2007} }

- Published 2007

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… CONTINUE READING