Cohen-Macaulayness of powers of two-dimensional squarefree monomial ideals

TL;DR

This paper provides combinatorial characterizations for when powers of two-dimensional squarefree monomial ideals, viewed as graph Stanley-Reisner ideals, are Cohen-Macaulay, linking algebraic properties to graph structures.

Contribution

It introduces new combinatorial criteria to determine Cohen-Macaulayness of powers of these ideals based on the associated graph structure.

Findings

Characterization of Cohen-Macaulayness for ordinary powers

Characterization of Cohen-Macaulayness for symbolic powers

Connection between graph properties and algebraic Cohen-Macaulayness

Abstract

Two-dimensional squarefree monomial ideals can be seen as the Stanley-Reisner ideals of graphs. The main results of this paper are combinatorial characterizations for the Cohen-Macaulayness of ordinary and symbolic powers of such an ideal in terms of the associated graph.