Minimal relative Hilbert-Kunz multiplicity
Watanabe, Kei-ichi ; Yoshida, Ken-ichi
Illinois J. Math., Tome 48 (2004) no. 3, p. 273-294 / Harvested from Project Euclid
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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: $\bbP^{r-1} \times \bbP^{s-1} \hookrightarrow \bbP^{rs-1}$.
Publié le : 2004-01-15
Classification:  13D40,  13A35,  13H10,  13H15 
@article{1258136184,
     author = {Watanabe, Kei-ichi and Yoshida, Ken-ichi},
     title = {Minimal relative Hilbert-Kunz multiplicity},
     journal = {Illinois J. Math.},
     volume = {48},
     number = {3},
     year = {2004},
     pages = { 273-294},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258136184}
}

Watanabe, Kei-ichi; Yoshida, Ken-ichi. Minimal relative Hilbert-Kunz multiplicity. Illinois J. Math., Tome 48 (2004) no. 3, pp.  273-294. http://gdmltest.u-ga.fr/item/1258136184/