Crepant resolution of trihedral singularities

Abstract

The purpose of this paper is to construct a crepant resolution of quotient singularities by trihedral groups ( finite subgroups of SL(3,C) of certain type ), and prove that each Euler number of the minimal model is equal to the number of conjugacy classes. Trihedral singularities are 3-dimensional version of D_n-singularities, and they are non-isolated and many of them are not complete intersections. The resolution is similar to one of D_n-singularities. There is a nice combination of the toric resolution and Calabi-Yau resolution.