A Note on Cohen–Macaulayness of Stanley–Reisner Rings with Serre's Condition (S 2)
A Note on Cohen–Macaulayness of Stanley–Reisner Rings with Serre's Condition (S 2)
复制标题
DOI：
10.1080/00927870701716124
复制
发表时间：
2008-01
影响因子：
0.7
通讯作者：
N. Terai;KEN-ICHI Yoshida
中科院分区：
文献类型：
--
作者：
N. Terai;KEN-ICHI Yoshida
设Δ是顶点集V = {1，2，.，n}上的（d − 1）维单纯复形。利用亚历山大对偶，证明了Stanley-Reisner环k[Δ]是Cohen-Macaulay环，如果它满足Serre条件（S2），且重数e（k[Δ]）“充分大”，即，.我们还证明了如果e（k[Δ]）≤ 3d − 2且分次Betti数β2，d+2（k[Δ]）为零，则Castelnuovo-Mumford正则性reg k[Δ]小于d。
Let Δ be a (d − 1)-dimensional simplicial complex on the vertex set V = {1, 2,…, n}. In this article, using Alexander duality, we prove that the Stanley–Reisner ring k[Δ] is Cohen–Macaulay if it satisfies Serre's condition (S 2) and the multiplicity e(k[Δ]) is “sufficiently large”, that is, . We also prove that if e(k[Δ]) ≤ 3d − 2 and the graded Betti number β2, d+2(k[Δ]) vanishes, then the Castelnuovo–Mumford regularity reg k[Δ] is less than d.