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

Mordechai Katzman; Gennady Lyubeznik; Wenliang Zhang

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

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

Mordechai Katzman, Gennady Lyubeznik, Wenliang Zhang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We prove a result relating the Jacobian ideal and the generalized test ideal associated to a principal ideal in R = k[x₁,..., x_n] with [k: k^p] < ∞ or in R = k[[x₁,..., 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.

Original language	English (US)
Pages (from-to)	4193-4197
Number of pages	5
Journal	Proceedings of the American Mathematical Society
Volume	139
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9939-2011-10897-9
State	Published - Dec 2011

Keywords

F-jumping coefficient
Jacobian ideal
Test ideal

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10.1090/S0002-9939-2011-10897-9

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N2 - We prove a result relating the Jacobian ideal and the generalized test ideal associated to a principal ideal in R = k[x1,..., xn] with [k: kp] < ∞ or in R = k[[x1,..., xn]] 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.

AB - We prove a result relating the Jacobian ideal and the generalized test ideal associated to a principal ideal in R = k[x1,..., xn] with [k: kp] < ∞ or in R = k[[x1,..., xn]] 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.

KW - F-jumping coefficient

KW - Jacobian ideal

KW - Test ideal

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

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