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 language | English |
|---|---|
| Article number | 099 |
| Number of pages | 21 |
| Journal | SIGMA: Symmetry, Integrability and Geometry: Methods and Applications |
| Volume | 17 |
| Early online date | 10 Nov 2021 |
| DOIs | |
| Publication status | Published - 10 Nov 2021 |
Bibliographical note
Funding Information:The authors are grateful to Michel van den Bergh, Hiraku Nakajima, Yukinobu Toda, Michael Wemyss and the anonymous referees for questions, comments and suggestions. A.C. was supported by the Leverhulme Trust grant RPG-2021-149; S.G. was supported by an Aker Scholarship; Á.Gy. and B.Sz. were supported by the EPSRC grant EP/R045038/1. Á.Gy. was also supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sk lodowska-Curie grant agreement No. 891437.
Keywords
- Cornering
- Kleinian orbifold
- Preprojective algebra
- Quiver variety
- Quot scheme
ASJC Scopus subject areas
- Analysis
- Mathematical Physics
- Geometry and Topology