A weak version of the McKay correspondence for cyclic quotient singularities

Abstract

Let G be a finite subgroup of SL(n,C). If a quotient variety C^n/G has a crepant resolution, then its Euler number equals to the number of conjugacy classes of G, which is a weak version of the McKay correspondence. In this paper, we generalize this correspondence to a finite cyclic group of GL(n,C). We construct this correspondence using certain toric resolutions obtained through continued fractions.