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- W4225162140 abstract "It is well known that a $2$-dimensional cyclic quotient singularity $overline{W}$ has the same singularity category as a finite dimensional associative algebra $overline{R}$ introduced by Kalck and Karmazyn. We study the deformations of the algebra $overline{R}$ induced by the deformations of the surface $overline{W}$ to a smooth surface. We show that they are Morita--equivalent to path algebras $hat{R}$ of acyclic quivers for general smoothings within each irreducible component of the versal deformation space of $overline{W}$ (as described by Koll'ar and Shepherd-Barron). Furthermore, $hat{R}$ is semi-simple if and only if the smoothing is $mathbb{Q}$-Gorenstein (one direction is due to Kawamata). We provide many applications. For example, we describe strong exceptional collections of length $10$ on all Dolgachev surfaces and classify admissible embeddings of derived categories of quivers into derived categories of rational surfaces." @default.
- W4225162140 created "2022-05-01" @default.
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- W4225162140 date "2022-04-27" @default.
- W4225162140 modified "2023-09-27" @default.
- W4225162140 title "Categorical aspects of the Koll'ar--Shepherd-Barron correspondence" @default.
- W4225162140 doi "https://doi.org/10.48550/arxiv.2204.13225" @default.
- W4225162140 hasPublicationYear "2022" @default.
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