## Illinois Journal of Mathematics

### Minimal relative Hilbert-Kunz multiplicity

#### 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: $\bbP^{r-1} \times \bbP^{s-1} \hookrightarrow \bbP^{rs-1}$.

#### Article information

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

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258136184

Digital Object Identifier
doi:10.1215/ijm/1258136184

Mathematical Reviews number (MathSciNet)
MR2048225

Zentralblatt MATH identifier
1089.13007

#### Citation

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. https://projecteuclid.org/euclid.ijm/1258136184