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Hilbert-Kunz Multiplicity of Two-Dimensional Local Rings

Published online by Cambridge University Press:  22 January 2016

Kei-Ichi Watanabe  and
Ken-Ichi Yoshida
Kei-Ichi Watanabe
Affiliation:
Department of Mathematics, College of Humanities and Sciences, Nihon University, Setagaya-ku, Tokyo 156-0045, Japan, [email protected]
Ken-Ichi Yoshida
Affiliation:
Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan, [email protected]
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Abstract

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We study the behavior of Hilbert-Kunz multiplicity for powers of an ideal, especially the case of stable ideals and ideals in local rings of dimension 2. We can characterize regular local rings by certain equality between Hilbert-Kunz multiplicity and usual multiplicity.

We show that rings with “minimal” Hilbert-Kunz multiplicity relative to usual multiplicity are “Veronese subrings” in dimension 2.

Keywords

13D4013A3513H1013H1514B05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 162 , June 2001 , pp. 87 - 110
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2001

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