Quot schemes for Kleinian orbifolds

Alastair Craw, Balazs Szendroi, Søren Gammelgaard, Ádám Gyenge

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Abstract

For a finite subgroup Γ⊂SL(2,ℂ), we identify fine moduli spaces of certain cornered quiver algebras, defined in earlier work, with orbifold Quot schemes for the Kleinian orbifold [ℂ2/Γ]. We also describe the reduced schemes underlying these Quot schemes as Nakajima quiver varieties for the framed McKay quiver of Γ, taken at specific non-generic stability parameters. These schemes are therefore irreducible, normal and admit symplectic resolutions. Our results generalise our previous work on the Hilbert scheme of points on ℂ2/Γ; we present arguments that completely bypass the ADE classification
Original languageEnglish
Article number099
Number of pages21
JournalSIGMA: Symmetry, Integrability and Geometry: Methods and Applications
Volume17
Early online date10 Nov 2021
DOIs
Publication statusPublished - 10 Nov 2021

Keywords

  • Cornering
  • Kleinian orbifold
  • Preprojective algebra
  • Quiver variety
  • Quot scheme

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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