Cohen-Macaulayness of generically complete intersection monomial ideals

TL;DR

This paper investigates when certain monomial ideals, associated with specific simplicial complexes, possess the Cohen-Macaulay property, providing insights into their algebraic and combinatorial structure.

Contribution

It characterizes the Cohen-Macaulayness of generically complete intersection monomial ideals with fixed radical, linking algebraic properties to combinatorial structures.

Findings

Identifies conditions for Cohen-Macaulayness in these monomial ideals

Connects algebraic properties to the topology of associated simplicial complexes

Provides criteria for specific classes of ideals with fixed radical

Abstract

In this paper we discuss the problem of characterizing the Cohen-Macaulay property of certain families of monomial ideals with fixed radical. More precisely, we consider generically complete intersection monomial ideals whose radical corresponds to special classes of simplicial complexes.