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

Abstract

AbstractLetS=K[x1,x2,…,xn] be a polynomial ring over a fieldK. Let Δ be a simplicial complex whose vertex set is contained in {1, 2,…,n}. For an integerk≥ 0, we investigate thek-Buchsbaum property of residue class ringsS/I(t); andS/Itfor the Stanley-Reisner idealI=IΔ. We characterize thek-Buchsbaumness of such rings in terms of the simplicial complex Δ and the powert. We also give a characterization in the case whereIis the edge ideal of a simple graph.