Terminal Quotient Singularities in Dimension three via variation of GIT

TL;DR

This paper demonstrates that the economic resolution of a three-dimensional terminal quotient singularity can be realized as a specific component of a moduli space of G-equivariant objects, using King stability conditions.

Contribution

It establishes a novel link between economic resolutions of terminal quotient singularities and moduli spaces via GIT variation and King stability.

Findings

Economic resolution is isomorphic to a component of a G-equivariant moduli space.

Uses King stability condition to characterize the resolution.

Provides a new perspective on singularity resolutions in algebraic geometry.

Abstract

A 3-fold terminal quotient singularity X=C^3/G admits the economic resolution Y-> X, which is "close to being crepant". This paper proves that the economic resolution Y is isomorphic to a distinguished component of a moduli space of certain G-equivariant objects using the the King stability condition $\theta$ introduced by K\k{e}dzierski.