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

Katzman, Mordechai; Lyubeznik, Gennady; Zhang, Wenliang

doi:10.1090/S0002-9939-2011-10897-9

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.

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