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

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

1997-04-10

arxiv.org/abs/alg-geom/9704007v1

Mathematics

Algebraic Geometry

revised version of MPI-preprint 97/4, 35 pages, 13 figures, latex2e-file (preprint.tex), macro packages and eps-files

Scientific paper

For Gorenstein quotient spaces $C^d/G$, a direct generalization of the classical McKay correspondence in dimensions $d\geq 4$ 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 which 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.

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