Terminal Quotient Singularities in Dimension three via variation of GIT

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.