Eyal Markman
Published 2000-09-11, updated 2001-04-21Version 4
Let M be a moduli space of stable sheaves on a K3 or Abelian surface S. We express the class of the diagonal in the cartesian square of M in terms of the Chern classes of a universal sheaf. Consequently, we obtain generators of the cohomology ring of M. When S is a K3 and M is the Hilbert scheme of length n subschemes, this set of generators is sufficiently small in the sense that there aren't any relations among them in the stable cohomology ring. When S is the cotangent bundle of a Riemann surface, we recover the result of T. Hausel and M. Thaddeus: The cohomology ring of the moduli spaces of Higgs bundles is generated by the universal classes.
Comments: Latex, 23 pages. The introduction is expanded, the coefficient in part 3 of Theorem 1 is corrected, plus several other minor changes
Journal: Journal fur die reine und angewandte Mathematik 544 (2002), 61-82
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