Comparing Hilbert depth of $I$ with Hilbert depth of $S/I$. III

Abstract

Let $I$ be a squarefree monomial ideal of $S=K[x_1,\dots ,x_n]$. We prove that if $\mathrm{hdepth}(S/I)\le 8$ or $n\le 10$ then $\mathrm{hdepth}(I)\ge \mathrm{hdepth}(S/I)-1$.

31 pages; minor corrections