Homology multipliers and the relation type of parameter ideals
Abstract
We study the relation type question, raised by C. Huneke, which asks whether for a complete equidimensional local ring R there exists a uniform bound for the relation type of parameter ideals. Wang gave a positive answer to this question when the non-Cohen-Macaulay locus of R, denoted by NCM(R), has dimension zero. We first present an example, due to the first author, which gives a negative answer to the question when dim NCM(R) is at least 2. The major part of our work then is to investigate the remaining case, i.e., when dim NCM(R) = 1. We introduce the notion of homology multipliers and show that the question has a positive answer when R/A(R) is a domain, where A(R) is the ideal generated by all homology multipliers in R. In a more general context, we also discuss many interesting properties of homology multipliers.
Keywords
Cite
@article{arxiv.math/0501477,
title = {Homology multipliers and the relation type of parameter ideals},
author = {Ian M. Aberbach and Laura Ghezzi and Huy Tai Ha},
journal= {arXiv preprint arXiv:math/0501477},
year = {2007}
}
Comments
To appear in Pacific J. Math. 35 pages