An inequality involving tight closure and parameter ideals

Catalin Ciuperca; Florian Enescu

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arXiv · math/0306349

An inequality involving tight closure and parameter ideals

Catalin Ciuperca·Florian Enescu

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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.

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Catalin Ciuperca, Florian Enescu. 2003-06-24. An inequality involving tight closure and parameter ideals. https://arxiv.org/abs/math/0306349

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