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

Abstract

Let \(a_1,..., a_n\) be positive integers and let \(\Delta= NP(a_1,..., a_n)\) be the Newton polyhedron associated to these integers, that is, the convex hull in \(\mathbb{R}^{n}\) of the axial points that have \(a_i\) in the \(x_i\)-axis. We give some characterization of the minimal elements of \(\Delta\), and then use this characterization to give an alternative simpler proof of a main result of [7] on the normality of monomial ideals.