Minimal lattice points in the Newton polyhedron and application to normal ideals

Abstract

Let a1,...,an be positive integers and let ∆=NP(a1,...,an) be the Newton polyhedron associated to these integers, that is, the convex hull in Rn of the axial points that haveaiin the xi-axis. We give some characterization of the minimal elements of ∆, and then use this characterization to give an alternative simpler proof of a main result of [7] on the normality of monomial ideals.