Quot schemes for Kleinian orbifolds

Abstract

For a finite subgroup $\Gamma \subset \mathrm{SL}(2,\mathbb{C})$, we identify fine moduli spaces of certain cornered quiver algebras, defined in earlier work, with orbifold Quot schemes for the Kleinian orbifold $[{\mathbb{C}}^2/\Gamma ]$. We also describe the reduced schemes underlying these Quot schemes as Nakajima quiver varieties for the framed McKay quiver of $\Gamma$, 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 ${\mathbb{C}}^2/\Gamma$; we present arguments that completely bypass the ADE classification.

Inaccuracy corrected

References in corpus (2)

• Quiver Varieties and Branching
• Geometric construction of representations of affine algebras