On crepant resolutions of 2-parameter series of Gorenstein cyclic quotient singularities

Details On crepant resolutions of 2-parameter series of Gorenstein cyclic quotient singularities On crepant resolutions of 2-parameter series of Gorenstein cyclic quotient singularities

1998-03-20

arxiv.org/abs/math/9803096v1

Results in Math. 33, (1998), 208-265

Mathematics

Algebraic Geometry

52 pages. 3 Figures. LaTeX 2e with AMS and epsfig macros. Also available as ZIB Preprint

Scientific paper

An immediate generalization of the classical McKay correspondence for Gorenstein quotient spaces $\Bbb{C}^{r}/G$ in dimensions $r\geq 4$ would primarily demand the existence of projective, crepant, full desingularizations. Since this is not always possible, it is natural to ask about special classes of such quotient spaces which would satisfy the above property. In this paper we give explicit necessary and sufficient conditions under which 2-parameter series of Gorenstein cyclic quotient singularities have torus-equivariant resolutions of this specific sort in all dimensions.

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