Four generated, squarefree, monomial ideals

Abstract

Let $I⊋J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\ge d$, resp. $\ge d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of degrees $\ge d+1$, or by four special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\le d+1$ then the usual depth of $I/J$ is $\le d+1$ too.

to appear in "Bridging Algebra, Geometry, and Topology", Editors Denis Ibadula, Willem Veys, Springer Proceed. in Math. and Statistics, 96, 2014