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arXiv · 1004.3411

A generalization of a theorem of G. K. White

Victor Batyrev·Johannes Hofscheier
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Abstract

An n-dimensional simplex Δ in \R^n is called empty lattice simplex if Δ\cap\Z^n is exactly the set of vertices of Δ. A theorem of G. K. White shows that if n=3 then any empty lattice simplex Δ\subset\R^3 is isomorphic up to an unimodular affine linear transformation to a lattice tetrahedron whose all vertices have third coordinate 0 or 1. In this paper we prove a generalization of this theorem for an arbitrary odd dimension n=2d-1 which in some form was conjectured by Sebő and Borisov. This result implies a classification of all 2d-dimensional isolated Gorenstein cyclic quotient singularities with minimal log-discrepancy at least d.

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Victor Batyrev, Johannes Hofscheier. 2010-04-20. A generalization of a theorem of G. K. White. https://arxiv.org/abs/1004.3411

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