Buchsbaum Stanley–Reisner Rings and Cohen–Macaulay Covers
Buchsbaum Stanley–Reisner Rings and Cohen–Macaulay Covers
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DOI：
10.1080/00927870600651638
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发表时间：
2006-06
影响因子：
0.7
通讯作者：
N. Terai;KEN-ICHI Yoshida
中科院分区：
文献类型：
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作者：
N. Terai;KEN-ICHI Yoshida
首先，我们给出了BuchsbaumStanley-Reisner环具有线性分解的一个新的判别准则。其次，我们证明了每一个初始度为d的d − 1维复形Δ包含在同一维Cohen-Macaulay复形中，该复形的d − 1阶约化同调同构于Δ。我们称这样的单纯复形为Δ的Cohen-Macaulay覆盖。证明了当Δ是Buchsbaum时，Δ与它的Cohen-Macaulay覆盖之间的所有中间复形都是Buchsbaum.作为应用，我们确定了初始度为3的三维BuchsbaumStanley-Reisner环的h-向量.
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.