Noncommutative projective partial resolutions and quiver varieties
| Autor: | Gammelgaard, Søren, Gyenge, Ádám |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\Gamma\in \mathrm{SL}_2(\mathbb{C})$ be a finite subgroup. We introduce a class of projective noncommutative surfaces $\mathbb{P}^2_I$, indexed by a set of irreducible $\Gamma$-representations. Extending the action of $\Gamma$ from $\mathbb{C}^2$ to $\mathbb{P}^2$, we show that these surfaces generalise both $[\mathbb{P}^2/\Gamma]$ and $\mathbb{P}^2/\Gamma$. We prove that isomorphism classes of framed torsion-free sheaves on any $\mathbb{P}^2_I$ carry a canonical bijection to the closed points of appropriate Nakajima quiver varieties. In particular, we provide geometric interpretations for a class of Nakajima quiver varieties using noncommutative geometry. Our results partially generalise several previous results on such quiver varieties. Comment: 29 pages. Comments are welcome v2: corrected several small mistakes and typos |
| Databáze: | arXiv |
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