A new equivalence between singularity categories of commutative algebras
Algebraic Geometry
2021-08-10 v2 Commutative Algebra
Representation Theory
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.
Keywords
Cite
@article{arxiv.2103.06584,
title = {A new equivalence between singularity categories of commutative algebras},
author = {Martin Kalck},
journal= {arXiv preprint arXiv:2103.06584},
year = {2021}
}
Comments
9 pages, final version, minor changes and improvements of the presentation, appendix discussing examples of group graded singular equivalences added, comments are always welcome!