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

Abstract

For a finite subgroup G of GLð2; CÞ, we consider the moduli space M y of G-constellations. It depends on the stability parameter y and if y 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 y for some generic y if and only if Y is dominated by the maximal resolution under the assumption that G is abelian or small. 2010 Mathematics Subject Classification. 14D20; 14E16; 14J17. Key words and phrases. G-constellation, quotient singularity, maximal resolution. G-constellations onthat H 0 ðEÞ is isomorphic to the regular representation of G as a C½G-module.