论文标题
广义的Cohen-Macaulay本地环中的小扰动
Small perturbations in generalized Cohen-Macaulay local rings
论文作者
论文摘要
令$（r，\ frak m）$为概括的cohen-macaulay local dimension $ d $，$ f_1，\ ldots，f_r $ a $ r $的参数系统的一部分。在本文中，我们给出了明确的数字$ n $，以使所有较低的本地共同体学模块的长度和$ r/（f_1，\ ldots，f_r）$的希尔伯特功能在我们将序列$ f_1，\ ldots，\ ldots，f_r $ by $ \ varepsilon_1，\ ldeps \ ldeps \ ldots中保留下来。 m}^n $。第二个断言扩展了srinivas和Trivedi的先前结果，用于广义的Cohen-Macaulay环。
Let $(R, \frak m)$ be a generalized Cohen-Macaulay local ring of dimension $d$, and $f_1, \ldots, f_r$ a part of system of parameters of $R$. In this paper we give explicit numbers $N$ such that the lengths of all lower local cohomology modules and the Hilbert function of $R/(f_1, \ldots, f_r)$ are preserved when we perturbs the sequence $f_1, \ldots, f_r$ by $\varepsilon_1, \ldots, \varepsilon_r \in {\frak m}^N$. The second assertion extends a previous result of Srinivas and Trivedi for generalized Cohen-Macaulay rings.
