Classification of objects in the singularity categories of rational double points in arbitrary characteristics
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 provide methods to handle the homotopy categories of matrix factorizations of isolated hypersurface singularities with computer algebra systems.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.