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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Bibliographic Details
Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2021
Main Authors: Craw, Alastair, Gammelgaard, Søren, Gyenge, Ádám, Szendrői, Balázs
Format: Article
Language:English
Published: Інститут математики НАН України 2021
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
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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.
ISSN:1815-0659