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arXiv 2007.15772math.AC
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关于微分模的Rees代数的Cohen-Macaulay性质

On the Cohen-Macaulay property of the Rees algebra of the module of differentials

Alessandra Costantini, Tan Dang

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9 pages
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摘要：

设$R$是域$k$上的本质有限型代数，$Ω_k(R)$是其在$k$上的Kähler微分模.若$R$是齐次完全交，且$\mathrm{char}(k)=0$是齐次完全交，则当$Ω_k(R)$的Rees代数是Cohen-Macaulay代数时，$Ω_k(R)$是线性型的，且局部地在每一齐次素数$\mathfrak{p}$处，$R_{\mathfrak{p}}$的嵌入维数至多为其维数的两倍.

英文摘要：

Let $R$ be an algebra essentially of finite type over a field $k$ and let $Ω_k(R)$ be its module of Kähler differentials over $k$. If $R$ is a homogeneous complete intersection and $\mathrm{char}(k)=0$, we prove that $Ω_k(R)$ is of linear type whenever its Rees algebra is Cohen-Macaulay and locally at every homogeneous prime $\mathfrak{p}$ the embedding dimension of $R_{\mathfrak{p}}$ is at most twice its dimension.

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