Quot schemes for Kleinian orbifolds
| Autor: | Craw, Alastair, Gammelgaard, Søren, Gyenge, Ádám, Szendrői, Balázs |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | SIGMA 17 (2021), 099, 21 pages |
| Druh dokumentu: | Working Paper |
| DOI: | 10.3842/SIGMA.2021.099 |
| Popis: | 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. Comment: Inaccuracy corrected |
| Databáze: | arXiv |
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