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A new equivalence between singularity categories of commutative algebras (2103.06584v2)

Published 11 Mar 2021 in math.AG, math.AC, and math.RT

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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