2010/04/20 by Victor Batyrev, Batyrev, Victor, Johannes Hofscheier +1
Mathematics · #11B68 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #Primary 52B20 #Secondary 14B05 #math.AG #math.CO #math.NT #msc:11B68 #msc:14B05 #msc:52B20
paper · pdf · doi:10.48550/arxiv.1004.3411
12 pages, 2 figures
arxiv created 2010/04/20 · arxiv updated 2010/04/21
An n-dimensional simplex Δ in \Rn is called empty lattice simplex if Δ∩\Zn 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⊂\R3 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.