Crepant Resolutions of 3-Dimensional Quotient Singularities via Cox Rings

We study Cox rings of crepant resolutions of quotient singularities C^3/G, where G is a finite subgroup of SL(3, C). We use them to obtain information on the geometric structure of these resolutions, number of different resolutions, and relations between them. In particular, we treat explicitly several examples where G contains elements of age 2.