Singularity categories via higher McKay quivers with potential

2024/04/01 by Liu, Junyang · 1 citation
#14B05 #16E45 #18G80 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2404.01171

Abstract

In 2018, Kalck and Yang showed that the singularity categories associated with 3-dimensional Gorenstein quotient singularities are triangle equivalent (up to direct summands) to small cluster categories associated with McKay quivers with potential. We introduce higher McKay quivers with potential and generalize Kalck and Yang's theorem to arbitrary dimensions. The singularity categories we consider occur as the stable categories of categories of maximal Cohen-Macaulay modules. We refine our description of the singularity categories by showing that these categories of maximal Cohen-Macaulay modules are equivalent to Higgs categories in the sense of Wu. Moreover, we describe the singularity categories in the non-Gorenstein case.

Cited by

• Calabi-Yau structures on derived and singularity categories of symmetric orders

Related

• Stable categories of Cohen-Macaulay modules and cluster categories
• Triangulated categories of Gorenstein cyclic quotient singularities
• Tilting and cluster tilting for quotient singularities
• Stable Categories of Graded Maximal Cohen-Macaulay Modules over Noncommutative Quotient Singularities
• The singularity category of an exact category applied to characterize Gorenstein schemes