## Kodai Mathematical Journal

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

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

#### 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