Small perturbations in generalized Cohen-Macaulay local rings

Abstract

Let (R,m) be a generalized Cohen-Macaulay local ring of dimension d, and f1,…,fr 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/(f1,…,fr) are preserved when we perturb the sequence f1,…,fr by ε1,…,εr∈mN. The second assertion extends a previous result of Srinivas and Trivedi for generalized Cohen-Macaulay rings.