On the extremal Betti numbers of squarefree monomial ideals

TL;DR

This paper characterizes the possible extremal Betti numbers of squarefree strongly stable ideals in polynomial rings, providing a numerical description of their values and positions.

Contribution

It offers a new numerical characterization of extremal Betti numbers for squarefree strongly stable ideals, advancing understanding of their algebraic structure.

Findings

Provides a numerical characterization of extremal Betti numbers.

Identifies possible values and positions of extremal Betti numbers.

Enhances understanding of the algebraic properties of squarefree strongly stable ideals.

Abstract

Let $K$ be a field and $S = K[x_1,\dots,x_n]$ be a polynomial ring over $K$. We discuss the behaviour of the extremal Betti numbers of the class of squarefree strongly stable ideals. More precisely, we give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of such a class of squarefree monomial ideals.