Classification of objects in the singularity categories of rational double points in arbitrary characteristics
Algebraic Geometry
2026-05-26 v1 Representation Theory
Abstract
We study rational double points over algebraically closed fields in arbitrary characteristics and completely classify the indecomposable objects in their singularity categories, which correspond to the vertices in their Auslander-Reiten quivers. Along the way, we present an alternative proof determining the configuration of these Auslander-Reiten quivers, and establish methods to handle the homotopy categories of matrix factorizations of isolated hypersurface singularities with computer algebra systems.
Keywords
Cite
@article{arxiv.2605.25896,
title = {Classification of objects in the singularity categories of rational double points in arbitrary characteristics},
author = {Yuta Takashima},
journal= {arXiv preprint arXiv:2605.25896},
year = {2026}
}