Illinois Journal of Mathematics

Minimal relative Hilbert-Kunz multiplicity

Kei-ichi Watanabe and Ken-ichi Yoshida

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In this paper we ask the following question: What is the minimal value of the difference $\ehk(I) - \ehk(I')$ for ideals $I' \supseteq I$ with $l_A(I'/I) =1$? In order to answer to this question, we define the notion of minimal relative Hilbert-Kunz multiplicity for strongly $F$-regular rings. We calculate this invariant for quotient singularities and for the coordinate rings of Segre embeddings: $\bbP^{r-1} \times \bbP^{s-1} \hookrightarrow \bbP^{rs-1}$.

Article information

Illinois J. Math., Volume 48, Number 1 (2004), 273-294.

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 13D40: Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series
Secondary: 13A35: Characteristic p methods (Frobenius endomorphism) and reduction to characteristic p; tight closure [See also 13B22] 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 13H15: Multiplicity theory and related topics [See also 14C17]


Watanabe, Kei-ichi; Yoshida, Ken-ichi. Minimal relative Hilbert-Kunz multiplicity. Illinois J. Math. 48 (2004), no. 1, 273--294. doi:10.1215/ijm/1258136184.

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