Noncommutative cyclic isolated singularities

Abstract

The question of whether a noncommutative graded quotient singularity A G A^G is isolated depends on a subtle invariant of the G G -action on A A , called the pertinency. We prove a partial dichotomy theorem for isolatedness, which applies to a family of noncommutative quotient singularities arising from a graded cyclic action on the ( − 1 ) (-1) -skew polynomial ring. Our results generalize and extend some results of Bao, He, and the third-named author and results of Gaddis, Kirkman, Moore, and Won.