### Existence of vector bundles and global resolutions for singular surfaces, by Stefan Schroeer and Gabriele Vezzosi

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.

Stefan Schroeer <s.schroeer@ruhr-uni-bochum.de>

Gabriele Vezzosi <vezzosi@dm.unibo.it>