广义截断多胞形的Stanley-Reisner环及其矩角流形
Stanley--Reisner rings of generalised truncation polytopes and their moment-angle manifolds
摘要：
我们考虑单多面体$P=vc^{k}(Δ^{n_{1}}\times\ldots\timesΔ^{n_{r}})$，对于$n_1\ge\ldots\ge n_r\ge 1,r\ge 1,k\ge 0$，即单形乘积的$k$ -顶点割，称它们为{ \emph{generalized truncation polytopes} }.对于这些多面体，我们描述了相应的矩角流形$\mathcal Z_P$的上同调环，并探讨这种计算的一些拓扑后果。我们还研究了最小的非Goldness的斯坦利-Reisner环，并将其与属性的$\mathcal Z_P$是一个连接的总和领域的产品。
英文摘要：
We consider simple polytopes $P=vc^{k}(Δ^{n_{1}}\times\ldots\timesΔ^{n_{r}})$, for $n_1\ge\ldots\ge n_r\ge 1,r\ge 1,k\ge 0$, that is, $k$-vertex cuts of a product of simplices, and call them {\emph{generalized truncation polytopes}}. For these polytopes we describe the cohomology ring of the corresponding moment-angle manifold $\mathcal Z_P$ and explore some topological consequences of this calculation. We also examine minimal non-Golodness for their Stanley--Reisner rings and relate it to the property of $\mathcal Z_P$ being a connected sum of sphere products.
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