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Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces

Eyal Markman
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Abstract

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.

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Eyal Markman. 2001-04-21. Generators of the cohomology ring of moduli spaces of sheaves on symplectic surfaces. https://arxiv.org/abs/math/0009109

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