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 All Abelian Quotient C.i.-singularities Admit Projective Crepant Resolutions in All Dimensions

For Gorenstein quotient spaces C d =G, a direct generalization of the classical McKay correspondence in dimensions d 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 Gorenstei...

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

For Gorenstein quotient spaces C/G, a direct generalization of the classical McKay correspondence in dimensions d ≥ 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...

All Toric L.C.I.-Singularities Admit Projective Crepant Resolutions

It is known that the underlying spaces of all abelian quotient singularities which are embeddable as complete intersections of hypersurfaces in an affine space can be overall resolved by means of projective torus-equivariant crepant birational morphisms in all dimensions. In the present paper we extend this result to the entire class of toric l.c.i.-singularities. Our proof makes use of Nakajim...

All Toric L . C . I . - Singularities Admit

Crepant Resolution Conjecture in All Genera for Type a Singularities

Abstract. We prove an all genera version of the Crepant Resolution Conjecture of Ruan and Bryan-Graber for type A surface singularities. We are based on a method that explicitly computes Hurwitz-Hodge integrals described in an earlier paper and some recent results by Liu-Xu for some intersection numbers on the Deligne-Mumford moduli spaces. We also generalize our results to some three-dimension...