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arXiv · 2106.10115

Quot schemes for Kleinian orbifolds

Alastair Craw·Søren Gammelgaard·Ádám Gyenge·Balázs Szendrői
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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.

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Alastair Craw, Søren Gammelgaard, Ádám Gyenge, Balázs Szendrői. 2021-06-18. Quot schemes for Kleinian orbifolds. https://doi.org/10.3842/sigma.2021.099

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