Quot Schemes for Kleinian Orbifolds

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 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.