Existence of vector bundles and global resolutions for singular surfaces

Stefan Schröer, Gabriele Vezzosi
2004 Compositio Mathematica  
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 non-separated schemes, usually many coherent
more » ... ally many coherent sheaves are not quotients of vector bundles.
doi:10.1112/s0010437x0300071x fatcat:f6rrxvjmuvftbckn5777xyounm