All toric l.c.i.-singularities admit projective crepant resolutions

Details All toric l.c.i.-singularities admit projective crepant resolutions All toric l.c.i.-singularities admit projective crepant resolutions

1998-12-03

arxiv.org/abs/math/9812025v2

Mathematics

Algebraic Geometry

33 pages, 13 eps-figures, LaTeX2e (revised 3/99: minor corrections and modifications)

Scientific paper

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 Nakajima's classification theorem and of some special techniques from toric and discrete geometry.

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