An inequality involving tight closure and parameter ideals
Commutative Algebra
2007-05-23 v1
Abstract
We establish an inequality involving colengths of the tight closure of ideals of systems of parameters in local rings with some mild conditions. As an application, we prove and refine a result by Goto and Nakamura, conjectured by Watanabe and Yoshida, which states that the Hilbert-Samuel multiplicity of a parameter ideal is greater than or equal to the colength of the tight closure of the ideal.
Cite
@article{arxiv.math/0306349,
title = {An inequality involving tight closure and parameter ideals},
author = {Catalin Ciuperca and Florian Enescu},
journal= {arXiv preprint arXiv:math/0306349},
year = {2007}
}
Comments
8 pages, to appear in Bull. London Math. Soc