On the extremal Betti numbers of squarefree monomial 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.