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

2017/10/11 by Ishii, Akira
#14D20 #14E16 #14J17 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.03911

Abstract

For a finite subgroup G of GL(2, \mathbb C), we consider the moduli space \mathcal M_θ of G-constellations. It depends on the stability parameter θ and if θ is generic it is a resolution of singularities of \mathbb C²/G. In this paper, we show that a resolution Y of \mathbb C²/G is isomorphic to \mathcal M_θ for some generic θ if and only if Y is dominated by the maximal resolution under the assumption that G is abelian or small.

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