Embedded Associated Primes of Powers of Square-free Monomial Ideals
Abstract
Description
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 beta_1, where beta_1 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=beta_1 +1. As an application, we investigate how these results relate to a conjecture of Conforti and Cornuéjols.
15 pages, changes have been made to the title, introduction, and background material, and an example has been added. To appear in JPAA
15 pages, changes have been made to the title, introduction, and background material, and an example has been added. To appear in JPAA