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

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

2011-11-11

arxiv.org/abs/1111.2880v2

Mathematics

Combinatorics

Introduction, last section and bibliography are revised

Scientific paper

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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