Triangulated categories of Gorenstein cyclic quotient singularities

TL;DR

This paper establishes an equivalence between the triangulated category of singularities for Gorenstein cyclic quotient singularities and a derived category of quiver representations, revealing a new connection in algebraic geometry.

Contribution

It introduces a novel equivalence between categories associated with Gorenstein cyclic quotient singularities and specific quiver representations, expanding understanding of their structure.

Findings

Proves an equivalence of triangulated categories for Gorenstein cyclic quotient singularities.

Connects the category of singularities with a derived category of quiver representations.

Provides a new perspective on the structure of singularities via quiver modifications.

Abstract

We prove an equivalence of triangulated categories between Orlov's triangulated category of singularities for a Gorenstein cyclic quotient singularity and the derived category of representations of a quiver with relations which is obtained from the McKay quiver by removing one vertex and half of the arrows.