Level property of ordinary and symbolic powers of Stanley-Reisner ideals

Abstract

In this paper, we prove that the t-th ordinary and/or symbolic power of a Stanley-Reisner ideal is level for some positive integer t≥3 if and only if IΔ is a complete intersection and equi-generated. For t=2, we give a characterization of level property of the second symbolic power IΔ(2) when Δ is a matroid complex of dimension one.