Ehrhart polynomials of polytopes and spectrum at infinity of Laurent polynomials

Abstract

Gathering different results from singularity theory, geometry and combinatorics, we show that the spectrum at infinity of a tame Laurent polynomial counts lattice points in polytopes and we deduce an effective algorithm in order to compute the Ehrhart polynomial of a simplex containing the origin as an interior point.

arXiv commentReferences updated. Two remarks on the distribution (unimodality, variance) of the spectrum at infinity added