A relation between number of integral points, volumes of faces and degree of the discriminant of smooth lattice polytopes

2011/11/11 by Dickenstein, Alicia, Nill, Benjamin, Vergne, Michèle
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1111.2880

Abstract

We present a formula for the degree of the discriminant of a smooth projective toric variety associated to a lattice polytope P, in terms of the number of integral points in the interior of dilates of faces of dimension greater or equal than \lceil \frac dim P 2 \rceil.

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