For a finite subgroup (Formula presented), 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 work [Algebr. Geom. 8 (2021), 680–704] on the Hilbert scheme of points on C2/Γ; we present arguments that completely bypass the ADE classification.
Quot schemes for kleinian orbifolds / A. Craw, S. Gammelgaard, A. Gyenge, B. Szendroi. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 17:(2021), pp. 099.1-099.21. [10.3842/SIGMA.2021.099]
Quot schemes for kleinian orbifolds
S. Gammelgaard;
2021
Abstract
For a finite subgroup (Formula presented), 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 work [Algebr. Geom. 8 (2021), 680–704] on the Hilbert scheme of points on C2/Γ; we present arguments that completely bypass the ADE classification.
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