Normality of Monomial Ideals

Abstract

Given the monomial ideal I=(x_1^{α_1},...,x_{n}^{α_{n}})\subset K[x_1,...,x_{n}] where α_{i} are positive integers and K a field and let J be the integral closure of I . It is a challenging problem to translate the question of the normality of J into a question about the exponent set Γ(J) and the Newton polyhedron NP(J). A relaxed version of this problem is to give necessary or sufficient conditions on α_1,...,α_{n} for the normality of J. We show that if α_{i}ε{s,l} with s and l arbitrary positive integers, then J is normal.