Kodai Mathematical Journal

Formulas of F-thresholds and F-jumping coefficients on toric rings

Daisuke Hirose

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Abstract

Mustaţă, Takagi and Watanabe define F-thresholds, which are invariants of a pair of ideals in a ring of characteristic p > 0. In their paper, it is proved that F-thresholds are equal to jumping numbers of test ideals on regular local rings. In this note, we give formulas of F-thresholds and F-jumping coefficients on toric rings. By these formulas, we prove that there exists an inequality between F-jumping coefficients and F-thresholds. In particular, we observe a difference between F-pure thresholds and F-thresholds on certain rings. As applications, we give a characterization of regularity for toric rings defined by simplicial cones, and we prove the rationality of F-thresholds on certain rings.

Article information

Source
Kodai Math. J., Volume 32, Number 2 (2009), 238-255.

Dates
First available in Project Euclid: 26 June 2009

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1245982906

Digital Object Identifier
doi:10.2996/kmj/1245982906

Mathematical Reviews number (MathSciNet)
MR2549545

Zentralblatt MATH identifier
1182.13006

Citation

Hirose, Daisuke. Formulas of F-thresholds and F-jumping coefficients on toric rings. Kodai Math. J. 32 (2009), no. 2, 238--255. doi:10.2996/kmj/1245982906. https://projecteuclid.org/euclid.kmj/1245982906


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