Geodesic
Quot Schemes for Kleinian Orbifolds
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\big[\mathbb{C}^2\!/\Gamma\big]$. 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 work [Algebr. Geom. 8 (2021), 680–704] on the Hilbert scheme of points on $\mathbb{C}^2/\Gamma$; we present arguments that completely bypass the ADE classification.
Keywords: Quot scheme, quiver variety, Kleinian orbifold, preprojective algebra, cornering. 
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     author = {Alastair Craw and S{\o}ren Gammelgaard and \'Ad\'am Gyenge and Bal\'azs Szendr\H{o}i},
     title = {Quot {Schemes} for {Kleinian} {Orbifolds}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2021},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a98/}
}
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Alastair Craw; Søren Gammelgaard; Ádám Gyenge; Balázs Szendrői. Quot Schemes for Kleinian Orbifolds. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a98/

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