Small perturbations in generalized Cohen-Macaulay local rings

Pham Hung Quy; Van Duc Trung

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arXiv · 2004.08873

Small perturbations in generalized Cohen-Macaulay local rings

Pham Hung Quy·Van Duc Trung

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Abstract

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.

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Pham Hung Quy, Van Duc Trung. 2020-04-19. Small perturbations in generalized Cohen-Macaulay local rings. https://arxiv.org/abs/2004.08873

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