Existence of vector bundles and global resolutions for singular surfaces

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We prove two results about vector bundles on singular algebraic surfaces. First, on proper surfaces there are vector bundles of rank two with arbitrarily large second Chern number and fixed determinant. Second, on separated normal surfaces any coherent sheaf is the quotient of a vector bundle. As a consequence, for such surfaces the Quillen K-theory of vector bundles coincides with the Waldhausen K-theory of perfect complexes. Examples show that, on nonseparated schemes, usually many coherent sheaves are not quotients of vector bundles.
Some minor corrections, comments and references added; to appear in Compositio Mathematica

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Algebraic Geometry, K-Theory and Homology, 14F05, 14J60, 14C35

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http://salesiana.dossiersoluciones.com/handle/123456789/63115

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0201128
 http://arxiv.org/abs/math/0201128
 Compositio Math. 140 (2004), 717-728.

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arXiv