Normality of Monomial Ideals

2010/09/03 by Al-Ayyoub, Ibrahim
#13P99 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1009.0786

Abstract

Given the monomial ideal I=(x₁^α₁,...,x_n^α_n)⊂ K[x₁,...,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 α₁,...,α_n for the normality of J. We show that if α_iεs,l with s and l arbitrary positive integers, then J is normal.

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