Abstract
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: $\bbP^{r-1} \times \bbP^{s-1} \hookrightarrow \bbP^{rs-1}$.
Citation
Kei-ichi Watanabe. Ken-ichi Yoshida. "Minimal relative Hilbert-Kunz multiplicity." Illinois J. Math. 48 (1) 273 - 294, Spring 2004. https://doi.org/10.1215/ijm/1258136184
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