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arXiv 0912.1089math.ACmath.CO
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满足Serre条件的单纯复形的H-向量

H-vectors of simplicial complexes with Serre's conditions

Satoshi Murai, Naoki Terai

备注：
To appear in Math. Res. Lett
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摘要：

研究了满足Serre条件（$S_r$）的单纯复形的$h$ -向量.我们说一个单纯复形$Δ$满足Serre条件（$S_r$），如果$\tilde H_i(\lk_Δ(F);K)=0$对所有的面$F \in Δ$和对所有的$i < \min \{r-1,\dim \lk_Δ(F)\}$，其中$\lk_Δ(F)$是$Δ$关于$F$的环，$\tilde H_i(Δ;K)$是$Δ$在域$K$上的约化同调群.本文的主要结果是：如果$Δ$满足Serre条件（$S_r$），则（i）$h_k(Δ)$对$k =0,1,...,r$非负，（ii）$\sum_{k\geq r}h_k(Δ)$非负.

英文摘要：

We study $h$-vectors of simplicial complexes which satisfy Serre's condition ($S_r$). We say that a simplicial complex $Δ$ satisfies Serre's condition ($S_r$) if $\tilde H_i(\lk_Δ(F);K)=0$ for all faces $F \in Δ$ and for all $i < \min \{r-1,\dim \lk_Δ(F)\}$, where $\lk_Δ(F)$ is the link of $Δ$ with respect to $F$ and where $\tilde H_i(Δ;K)$ is the reduced homology groups of $Δ$ over a field $K$. The main result of this paper is that if $Δ$ satisfies Serre's condition ($S_r$) then (i) $h_k(Δ)$ is non-negative for $k =0,1,...,r$ and (ii) $\sum_{k\geq r}h_k(Δ)$ is non-negative.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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