No abstract

We give an algorithmic description of the action of the Chern classes of tautological bundles on the cohomology of Hilbert schemes of points on a smooth surface within the framework of Nakajima's oscillator algebra. This leads to an identification of the cohomology ring of Hilb n (A 2 ) with a ring of explicitly given differential operators on a Fock space. We end with the computation of the top Segre classes of tautological bundles associated to line bundles on Hilb n up to n = 7, extending computations of Severi, LeBarz, Tikhomirov and Troshina and give a conjecture for the generating series.

International audienc

Moduli spaces of semistable sheaves on a K3 or abelian surface with respect to a general ample divisor are shown to be locally factorial, with the exception of symmetric products of a K3 or abelian surface and the class of moduli spaces found by O'Grady. Consequently, since singular moduli space that do not belong to these exceptional cases have singularities in codimension $\geq4$ they do no admit projective symplectic resolutions

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