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

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

2000-09-11

arxiv.org/abs/math/0009109v4

Journal fur die reine und angewandte Mathematik 544 (2002), 61-82

Mathematics

Algebraic Geometry

Latex, 23 pages. The introduction is expanded, the coefficient in part 3 of Theorem 1 is corrected, plus several other minor c

Scientific paper

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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