Tohoku Mathematical Journal

All toric local complete intersection singularities admit projective crepant resolutions

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

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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.

Article information

Source
Tohoku Math. J. (2), Volume 53, Number 1 (2001), 95-107.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178207533

Digital Object Identifier
doi:10.2748/tmj/1178207533

Mathematical Reviews number (MathSciNet)
MR1808643

Zentralblatt MATH identifier
1050.14044

Subjects
Primary: 14M25: Toric varieties, Newton polyhedra [See also 52B20]
Secondary: 14E15: Global theory and resolution of singularities [See also 14B05, 32S20, 32S45]

Citation

Dais, Dimitrios I.; Haase, Christian; Ziegler, Günter M. All toric local complete intersection singularities admit projective crepant resolutions. Tohoku Math. J. (2) 53 (2001), no. 1, 95--107. doi:10.2748/tmj/1178207533. https://projecteuclid.org/euclid.tmj/1178207533


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References

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