Existence of vector bundles and global resolutions for singular surfaces

Details Existence of vector bundles and global resolutions for singular surfaces Existence of vector bundles and global resolutions for singular surfaces

2002-01-15

arxiv.org/abs/math/0201128v2

Compositio Math. 140 (2004), 717-728.

Mathematics

Algebraic Geometry

Some minor corrections, comments and references added; to appear in Compositio Mathematica

Scientific paper

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.

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