Buchsbaum stanley-reisner rings and cohen-macaulay covers

First, we give a new criterion for Buchsbaum Stanley-Reisner rings to have linear resolutions. Next, we prove that every ( d - 1)-dimensional complex Δ of initial degree d is contained in the same dimensional Cohen-Macaulay complex whose ( d - 1)th reduced homology is isomorphic to that of Δ. We call such a simplicial complex a Cohen-Macaulay cover of Δ. And we also show that all the intermediate complexes between Δ and its Cohen-Macaulay cover are Buchsbaum provided that Δ is Buchsbaum. As an application, we determine the h -vectors of the 3-dimensional Buchsbaum Stanley-Reisner rings with initial degree 3.