Buchsbaum Stanley-Reisner rings and Cohen-Macaulay covers

摘要

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