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All toric local complete intersection singularities admit projective crepant resolutions. (English) Zbl 1050.14044

Summary: 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 [H. Nakajima, J. Tôhoku Math. J., II. Ser. 38, 85–98 (1986; Zbl 0604.14044)] and of some techniques from toric and discrete geometry.

MSC:

14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14E15 Global theory and resolution of singularities (algebro-geometric aspects)
14M10 Complete intersections
52B20 Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry)
14B05 Singularities in algebraic geometry

Citations:

Zbl 0604.14044
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References:

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