On graded stable derived categories of isolated Gorenstein quotient singularities

TL;DR

This paper demonstrates the existence of full exceptional collections in graded stable derived categories of certain Gorenstein quotient singularities, extending to non-isolated cases via equivariant categories.

Contribution

It establishes the presence of full exceptional collections in graded stable derived categories for Gorenstein isolated quotient singularities and their Veronese subrings, even in non-isolated cases.

Findings

Full exceptional collection exists for Gorenstein isolated quotient singularities.

Equivariant graded stable derived categories of Gorenstein Veronese subrings have full strong exceptional collections.

Results extend to non-isolated quotient singularities under group actions.

Abstract

We show the existence of a full exceptional collection in the graded stable derived category of a Gorenstein isolated quotient singularity using a result of Orlov (arXiv:math/0503632). We also show that the equivariant graded stable derived category of a Gorenstein Veronese subring of a polynomial ring with respect to an action of a finite group has a full strong exceptional collection, even if the corresponding quotient singularity is neither isolated nor Gorenstein.