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December 2007 Cohen-Macaulay local rings of embedding dimension $e+d-k$
Hsin-Ju Wang
Osaka J. Math. 44(4): 817-827 (December 2007).

Abstract

In this paper, we prove the following. Let $(R, \mathfrak{m})$ be a $d$-dimensional Cohen-Macaulay local ring with multiplicity $e$ and embedding dimension $v=e+d-k$, where $k \geq 3$ and $e-k>1$. If $\lambda(\mathfrak{m}^3/J\mathfrak{m}^2)=1$ and $\mathfrak{m}^3\subseteq J\mathfrak{m}$, where $J$ is a minimal reduction of $\mathfrak{m}$, then $3 \leq s \leq \tau +k-1$, where $s$ is the degree of the $h$-polynomial of $R$ and $\tau$ is the Cohen-Macaulay type of $R$.

Citation

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Hsin-Ju Wang. "Cohen-Macaulay local rings of embedding dimension $e+d-k$." Osaka J. Math. 44 (4) 817 - 827, December 2007.

Information

Published: December 2007
First available in Project Euclid: 7 January 2008

zbMATH: 1129.13017
MathSciNet: MR2383811

Subjects:
Primary: 13D40 , 13H10

Rights: Copyright © 2007 Osaka University and Osaka City University, Departments of Mathematics

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Vol.44 • No. 4 • December 2007
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