Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima quivers varieties.

Abstract. We establish the semistablity of Lazersfeld-Mukai bundles for some class of rank zero sheaves on a K3 surface, providing examples of moduli spaces which, locally around a singular point, are isomorphic to a quiver variety in the sense of Nakajima.

The singularities of these moduli spaces arise from the choice of a specific polarization and admit natural symplectic resolutions corresponding to the choice of a general polarization. We show that these resolutions correspond, via the above isomorphism, to natural symplectic resolutions of the quiver variety coming from variations of GIT quotients. This is joint work with E. Arbarello.