Classes of sequentially Cohen-Macaulay squarefree monomial ideals

TL;DR

This paper characterizes when completely squarefree lexsegment ideals are sequentially Cohen-Macaulay, providing minimal primary decompositions, homological invariant formulas, and demonstrating that critical squarefree monomial ideals possess this property.

Contribution

It offers a complete characterization of sequentially Cohen-Macaulay completely squarefree lexsegment ideals and computes their primary decompositions and homological invariants.

Findings

Critical squarefree monomial ideals are sequentially Cohen-Macaulay.

Complete primary decompositions for completely squarefree lexsegment ideals are provided.

Formulas for homological invariants of these ideals are derived.

Abstract

We compute the minimal primary decomposition for completely squarefree lexsegment ideals. We show that critical squarefree monomial ideals are sequentially Cohen-Macaulay. As an application, we give a complete characterization of the completely squarefree lexsegment ideals which are sequentially Cohen-Macaulay and we also derive formulas for some homological invariants of this class of ideals.