## Castelnuovo-Mumford regularity and the discreteness of $F$-jumping coefficients in graded rings

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- by Mordechai Katzman and Wenliang Zhang PDF
- Trans. Amer. Math. Soc.
**366**(2014), 3519-3533 Request permission

## Abstract:

In this paper we show that the sets of $F$-jumping coefficients of ideals form discrete sets in certain graded $F$-finite rings. We do so by giving a criterion based on linear bounds for the growth of the Castelnuovo-Mumford regularity of certain ideals. We further show that these linear bounds exist for one-dimensional rings and for ideals of (most) two-dimensional domains. We conclude by applying our technique to prove that all sets of $F$-jumping coefficients of all ideals in the determinantal ring given as the quotient by $2\times 2$ minors in a $2\times 3$ matrix of indeterminates form discrete sets.## References

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## Additional Information

**Mordechai Katzman**- Affiliation: Department of Pure Mathematics, Hicks Building, University of Sheffield, Sheffield S3 7RH, United Kingdom
- Email: M.Katzman@sheffield.ac.uk
**Wenliang Zhang**- Affiliation: Department of Mathematics, University of Nebraska, Lincoln, Nebraska 68588
- MR Author ID: 805625
- Email: wzhang15@unl.edu
- Received by editor(s): October 17, 2011
- Received by editor(s) in revised form: July 10, 2012
- Published electronically: March 4, 2014
- Additional Notes: The results in this paper were obtained while both authors enjoyed the hospitality of the School of Mathematics at the University of Minnesota. The first author also wishes to acknowledge support through Royal Society grant TG102669. The second author was supported in part by NSF Grant DMS #1068946.
- © Copyright 2014
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc.
**366**(2014), 3519-3533 - MSC (2010): Primary 13A35
- DOI: https://doi.org/10.1090/S0002-9947-2014-05918-7
- MathSciNet review: 3192605