Regularity of powers of Stanley-Reisner ideals of one-dimensional simplicial complexes

Abstract

Let $\Delta$ be a one-dimensional simplicial complex. Let $I_{\Delta }$ be the Stanley-Reisner ideal of $\Delta$. We prove that for all $s\ge 1$ and all intermediate ideals $J$ generated by $I_{\Delta }^s$ and some minimal generators of $I_{\Delta }^{(s)}$, we have $$\mathrm{reg}J=\mathrm{reg}{I}_{\Delta }^s=\mathrm{reg}{I}_{\Delta }^{(s)}.$$

19 pages, submitted