Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces

Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf epsilon exists over S x M, then its class [epsilon] admits a Kunneth decomposition as a class in the tensor product K-top(0)(epsilon) circle times K-top(0)(M) of the topological K-rings. The generators are the Chern classes of the Kunneth factors of [epsilon] in K-top(0)(M). The general case is similar. (c) 2006 Elsevier Inc. All rights reserved.