Buchsbaum Stanley–Reisner Rings and Cohen–Macaulay Covers

Abstract

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.

Keywords:

• Alexander duality
• Buchsbaum ring
• Cohen–Macaulay cover
• Linear resolution
• Multiplicity
• Regularity
• Stanley–Reisner ring

2000 Mathematics Subject Classification:

• Primary 13F55, 14E20
• Secondary 13H10, 13D02

ACKNOWLEDGMENT

The authors wish to thank the referee for many valuable comments.

Notes

Communicated by W. Bruns.