Cohen–Macaulayness of Generically Complete Intersection Monomial Ideals

Abstract

In this article, we try to understand which generically complete intersection monomial ideals with fixed radical are Cohen-Macaulay. We are able to give a complete characterization for a special class of simplicial complexes, namely the Cohen-Macaulay complexes without cycles in codimension 1. Moreover, we give sufficient conditions when the square-free monomial ideal has minimal multiplicity.