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

E. Arbarello, G. Saccà

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)649-703
Number of pages55
JournalAdvances in Mathematics
Volume329
DOIs
Publication statusPublished - 30 Apr 2018
Externally publishedYes

Keywords

  • K3 surfaces
  • Moduli spaces
  • Quiver varieties
  • Singularities
  • Symplectic resolution
  • Wall crossing

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