Stanley depth and symbolic powers of monomial ideals - Seyed Fakhari, S. A. (MATHEMATICA SCANDINAVICA, 2017)
The aim of this paper is to study the Stanley depth of symbolic powers of a squarefree monomial ideal. We prove that for every squarefree monomial ideal $I$ and every pair of integers $k, s≥ 1$, the inequalities $sdepth (S/I^{(ks)}) ≤ sdepth (S/I^{(s)})$ and $sdepth(I^{(ks)}) ≤ sdepth (I^{(s)})$ hold. If moreover $I$ is unmixed of height $d$, then we show that for every integer $k≥1$, $sdepth(I^{(k+d)})≤ sdepth(I^{{(k)}})$ and $sdepth(S/I^{(k+d)})≤ sdepth(S/I^{{(k)}})$. Finally, we consider the limit behavior of the Stanley depth of symbolic powers of a squarefree monomial ideal. We also introduce a method for comparing the Stanley depth of factors of monomial ideals.