The elementary transformation of vector bundles on regular schemes

• Autores: Takuro Abe
• Localización: Transactions of the American Mathematical Society, ISSN 0002-9947, Vol. 359, Nº 9, 2007, págs. 4285-4295
• Idioma: inglés
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• Resumen

  • 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.