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Minimal Hilbert-Kunz multiplicity

Kei-ichi Watanabe·Ken-ichi Yoshida
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Abstract

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

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Kei-ichi Watanabe, Ken-ichi Yoshida. 2003-03-12. Minimal Hilbert-Kunz multiplicity. https://arxiv.org/abs/math/0303139

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