All Abelian Quotient C.I.-Singularities Admit Projective Crepant Resolutions in All Dimensions

Abstract

For Gorenstein quotient spaces Cd/G, a direct generalization of the classical McKay correspondence in dimensionsd≥4 would primarily demand the existence of projective, crepant desingularizations. Since this turned out to be not always possible, Reid asked about special classes of such quotient spaces that would satisfy the above property. We prove that the underlying spaces of all Gorenstein abelian quotient singularities, which are embeddable as complete intersections of hypersurfaces in an affine space, have torus-equivariant projective crepant resolutions in all dimensions. We use techniques from toric and discrete geometry. © 1998 Academic Press.