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

Please always quote using this URN: urn:nbn:de:0297-zib-2708
  • \def\Bbb{\mathbb} For Gorenstein quotient spaces $\Bbb{C}^d/G$, 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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Metadaten
Author:Dimitrios I. Dais, Martin Henk, Günter M. Ziegler
Document Type:ZIB-Report
Date of first Publication:1997/01/17
Series (Serial Number):ZIB-Report (SC-97-01)
ZIB-Reportnumber:SC-97-01
Published in:Appeared in: Advances in Mathematics 139 (1998) 194-239
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