Tohoku Mathematical Journal
2001
March
SECOND SERIES VOL. 53, NO. 1

Tohoku Math. J.
53 (2001), 95-107

Title ALL TORIC LOCAL COMPLETE INTERSECTION SINGULARITIES ADMIT PROJECTIVE CREPANT RESOLUTIONS

Author Dimitrios I. Dais, Christian Haase and Günter M. Ziegler

(Received May 18, 1999, revised January 6, 2000)
Abstract. 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 local complete intersection singularities. Our strikingly simple proof makes use of Nakajima's classification theorem and of some techniques from toric and discrete geometry.

2000 Mathematics Subject Classification. Primary 14M25; Secondary 14E15, 14M10, 52B20.

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