Characterizations of Buchsbaum complexes

Letk be a field and an abstract simplicial complex with vertex set . In this article we study the structure of the Ext modules Ext _a ⁱ (A/m _(l ,k]) of the Stanley-Reisner ringk] whereA=kx ₁,...,x _n ] andm _l =(x _l ¹ ,...,x _l ⁿ ). Using this structure theorem we give a characterization of Buchsbaumness ofk] by means of the length of the modules Ext _A ⁱ (A/m _l ,k]). That isk] is Buchsbaum if and only if for allik], the length of the modules Ext _A ⁱ (A/m _l ,k]) is independent ofl.