Embedded Associated Primes of Powers of Square-free Monomial Ideals

2008/05/24 by Huy Tài Hà, Ha, Huy Tai, Susan Morey +1 · 5 citations
Computer Science · Mathematics · #13A17 #13C65 #13F55 #90C27 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.0805.3738

openalex publication_date 2008/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An ideal I in a Noetherian ring R is normally torsion-free if Ass(R/I^t)=Ass(R/I) for all natural numbers t. We develop a technique to inductively study normally torsion-free square-free monomial ideals. In particular, we show that if a square-free monomial ideal I is minimally not normally torsion-free then the least power t such that I^t has embedded primes is bigger than beta₁, where beta₁ is the monomial grade of I, which is equal to the matching number of the hypergraph H(I) associated to I. If in addition I fails to have the packing property, then embedded primes of I^t do occur when t=beta₁ +1. As an application, we investigate how these results relate to a conjecture of Conforti and Cornuéjols.

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