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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An upper bound on the number of $ F$-jumping coefficients of a principal ideal


Authors: Mordechai Katzman, Gennady Lyubeznik and Wenliang Zhang
Journal: Proc. Amer. Math. Soc. 139 (2011), 4193-4197
MSC (2010): Primary 13A35, 13N10
Published electronically: April 20, 2011
MathSciNet review: 2823064
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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.


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Additional 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
Email: gennady@math.umn.edu

Wenliang Zhang
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: wlzhang@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2011-10897-9
PII: S 0002-9939(2011)10897-9
Keywords: $F$-jumping coefficient, test ideal, Jacobian ideal
Received by editor(s): October 14, 2010
Published electronically: April 20, 2011
Communicated by: Harm Derksen
Article copyright: © Copyright 2011 American Mathematical Society