Singularities of moduli spaces of sheaves on K3 surfaces and Nakajima quiver varieties

© 2018 Elsevier Inc. The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non-generic polarization, with respect to which we consider stability, and admit...

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Bibliographic Details
Main Authors: Arbarello, E, Saccà, G
Other Authors: Massachusetts Institute of Technology. Department of Mathematics
Format: Article
Language:English
Published: Elsevier BV 2021
Online Access:https://hdl.handle.net/1721.1/135788
Description
Summary:© 2018 Elsevier Inc. The aim of this paper is to study the singularities of certain moduli spaces of sheaves on K3 surfaces by means of Nakajima quiver varieties. The singularities in question arise from the choice of a non-generic polarization, with respect to which we consider stability, and admit natural symplectic resolutions corresponding to choices of general polarizations. For sheaves that are pure of dimension one, we show that these moduli spaces are, locally around a singular point, isomorphic to a quiver variety and that, via this isomorphism, the natural symplectic resolutions correspond to variations of GIT quotients of the quiver variety.