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arXiv · 2103.06584

A new equivalence between singularity categories of commutative algebras

Martin Kalck
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Abstract

We construct a triangle equivalence between the singularity categories of two isolated cyclic quotient singularities of Krull dimensions two and three, respectively. This is the first example of a singular equivalence involving connected commutative algebras of odd and even Krull dimension. In combination with Orlov's localization result, this gives further singular equivalences between certain quasi-projective varieties of dimensions two and three, respectively.

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Martin Kalck. 2021-03-11. A new equivalence between singularity categories of commutative algebras. https://doi.org/10.1016/j.aim.2021.107913

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