An upper bound on the number of $F$-jumping coefficients of a principal ideal
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- by Mordechai Katzman, Gennady Lyubeznik and Wenliang Zhang
- Proc. Amer. Math. Soc. 139 (2011), 4193-4197
- DOI: https://doi.org/10.1090/S0002-9939-2011-10897-9
- Published electronically: April 20, 2011
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Abstract:
We prove a result relating the Jacobian ideal and the generalized test ideal associated to a principal ideal in $R=k[x_1,\dots ,x_n]$ with $[k:k^p]<\infty$ or in $R=k[[x_1,\dots ,x_n]]$ with an arbitrary field $k$ of characteristic $p>0$. As a consequence of this result, we establish an upper bound on the number of $F$-jumping coefficients of a principal ideal with an isolated singularity.References
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Bibliographic Information
- Mordechai Katzman
- Affiliation: Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, United Kingdom
- Email: M.Katzman@sheffield.ac.uk
- Gennady Lyubeznik
- Affiliation: Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
- MR Author ID: 117320
- Email: gennady@math.umn.edu
- Wenliang Zhang
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- MR Author ID: 805625
- Email: wlzhang@umich.edu
- Received by editor(s): October 14, 2010
- Published electronically: April 20, 2011
- Communicated by: Harm Derksen
- © Copyright 2011 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 139 (2011), 4193-4197
- MSC (2010): Primary 13A35, 13N10
- DOI: https://doi.org/10.1090/S0002-9939-2011-10897-9
- MathSciNet review: 2823064