Quot Schemes for Kleinian Orbifolds
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211428 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Quot Schemes for Kleinian Orbifolds. Alastair Craw, Søren Gammelgaard, Ádám Gyenge and Balázs Szendrői. SIGMA 17 (2021), 099, 21 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | 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.
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| ISSN: | 1815-0659 |