A new equivalence between singularity categories of commutative algebras
arXiv:2103.06584 · doi:10.1016/j.aim.2021.107913
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.
9 pages, final version, minor changes and improvements of the presentation, appendix discussing examples of group graded singular equivalences added, comments are always welcome!