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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2021 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2021
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/211428 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | 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| _version_ | 1862728645206867968 |
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| author | Craw, Alastair Gammelgaard, Søren Gyenge, Ádám Szendrői, Balázs |
| author_facet | Craw, Alastair Gammelgaard, Søren Gyenge, Ádám Szendrői, Balázs |
| citation_txt | Quot Schemes for Kleinian Orbifolds. Alastair Craw, Søren Gammelgaard, Ádám Gyenge and Balázs Szendrői. SIGMA 17 (2021), 099, 21 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-04-17T14:34:27Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-211428 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T14:34:27Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
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| spelling | Craw, Alastair Gammelgaard, Søren Gyenge, Ádám Szendrői, Balázs 2026-01-02T08:30:55Z 2021 Quot Schemes for Kleinian Orbifolds. Alastair Craw, Søren Gammelgaard, Ádám Gyenge and Balázs Szendrői. SIGMA 17 (2021), 099, 21 pages 1815-0659 2020 Mathematics Subject Classification: 16G20; 13A50; 14E16 arXiv:2106.10115 https://nasplib.isofts.kiev.ua/handle/123456789/211428 https://doi.org/10.3842/SIGMA.2021.099 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. The authors are grateful to Michel van den Bergh, Hiraku Nakajima, Yukinobu Toda, Michael Wemyss, and the anonymous referees for their questions, comments, and suggestions. A.C. was supported by the Leverhulme Trust grant RPG-2021-149; S.G. was supported by an Aker Scholarship; Á.Gy. and B.Sz. were supported by the EPSRC grant EP/R045038/1. Á.Gy. was also supported by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 891437. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quot Schemes for Kleinian Orbifolds Article published earlier |
| spellingShingle | Quot Schemes for Kleinian Orbifolds Craw, Alastair Gammelgaard, Søren Gyenge, Ádám Szendrői, Balázs |
| title | Quot Schemes for Kleinian Orbifolds |
| title_full | Quot Schemes for Kleinian Orbifolds |
| title_fullStr | Quot Schemes for Kleinian Orbifolds |
| title_full_unstemmed | Quot Schemes for Kleinian Orbifolds |
| title_short | Quot Schemes for Kleinian Orbifolds |
| title_sort | quot schemes for kleinian orbifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211428 |
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