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

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 $\lceil \frac {\dim P} 2 \rceil$.

Introduction, last section and bibliography are revised