Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces
Abstract
Description
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 E exists over SxM, then its class [E] admits a Kunneth decomposition as a class in the tensor product of the topological K-rings K(S) and K(M). The generators are the Chern classes of the Kunneth factors of [E] in K(M). The general case is similar
v3: Latex, 27 pages. Final version, to appear in Advances in Math. The proof of Lemma 21 is corrected and several other minor changes have been made. v2: Latex, 26 pages. The paper was split. The new version is a rewrite of the first three sections of version 1. The omitted results, about the monodromy of Hilbert schemes of point on a K3 surface, constitute part of the new paper arXiv:math.AG/0601304. v1: Latex, 53 pages
v3: Latex, 27 pages. Final version, to appear in Advances in Math. The proof of Lemma 21 is corrected and several other minor changes have been made. v2: Latex, 26 pages. The paper was split. The new version is a rewrite of the first three sections of version 1. The omitted results, about the monodromy of Hilbert schemes of point on a K3 surface, constitute part of the new paper arXiv:math.AG/0601304. v1: Latex, 53 pages