Homology multipliers and the relation type of parameter ideals

Details Homology multipliers and the relation type of parameter ideals Homology multipliers and the relation type of parameter ideals

2005-01-26

arxiv.org/abs/math/0501477v1

Mathematics

Commutative Algebra

To appear in Pacific J. Math. 35 pages

Scientific paper

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.

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