Regularity of linearly presented squarefree monomial ideals

TL;DR

This paper establishes a precise bound on the regularity of squarefree monomial ideals with linear presentations and confirms a related conjecture on their cohomological dimension under Serre's S2 condition.

Contribution

It provides a sharp bound for regularity and affirms a conjecture regarding cohomological dimension for a class of squarefree monomial ideals.

Findings

Proved a sharp regularity bound for ideals with linear presentation

Confirmed a positive answer to a question on cohomological dimension

Linked regularity bounds to Serre's S2 condition

Abstract

We prove a sharp bound for the regularity of a squarefree monomial ideal with a linear presentation. This result also answers in positive a question on the cohomological dimension of squarefree monomial ideals satisfying Serre's $S_2$-condition proposed by Dao and Takagi.