$G$-constellations and the maximal resolution of a quotient surface singularity

Abstract

For a finite subgroup G of GL(2, C), we consider the moduli space M θ of G-constellations. It depends on the stability parameter θ and if θ is generic it is a resolution of singularities of C 2 /G. In this paper, we show that a resolution Y of C 2 /G is isomorphic to M θ for some generic θ if and only if Y is s dominated by the maximal resolution under the assumption that G is abelian or small. G-constellations on C n DefinitionsLet V = C n be an affine space and G ⊂ GL(V ) a finite subgroup.