On the k-Buchsbaum property of powers of Stanley–Reisner ideals

Abstract

AbstractLet S = K[x1,x2,…,xn] be a polynomial ring over a field K. Let Δ be a simplicial complex whose vertex set is contained in {1, 2,…,n}. For an integer k ≥ 0, we investigate the k-Buchsbaum property of residue class rings S/I(t); and S/It for the Stanley-Reisner ideal I = IΔ. We characterize the k-Buchsbaumness of such rings in terms of the simplicial complex Δ and the power t. We also give a characterization in the case where I is the edge ideal of a simple graph.