Small perturbations in generalized Cohen-Macaulay local rings

Abstract

Let $(R,\mathfrak{m})$ be a generalized Cohen-Macaulay local ring of dimension $d$, and $f_1,\dots ,f_r$ 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 $R/(f_1,\dots ,f_r)$ are preserved when we perturbs the sequence $f_1,\dots ,f_r$ by ${\epsilon }_1,\dots ,{\epsilon }_r\in {\mathfrak{m}}^N$. The second assertion extends a previous result of Srinivas and Trivedi for generalized Cohen-Macaulay rings.

arXiv commentJ. Algebra