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# All abelian quotient c.i.-singularities admit projective crepant resolutions in all dimensions

## Dimitrios I. Dais and Martin Henk and Günter M. Ziegler – 1998

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.

Titel
All abelian quotient c.i.-singularities admit projective crepant resolutions in all dimensions
Verfasser
Dimitrios I. Dais and Martin Henk and Günter M. Ziegler
Datum
1998
Erschienen in
Advances in Mathematics, volume 139, pages 194-239
Art
Text