An upper bound on the number of -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

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove a result relating the Jacobian ideal and the generalized test ideal associated to a principal ideal in with or in with an arbitrary field of characteristic . As a consequence of this result, we establish an upper bound on the number of -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:
https://doi.org/10.1090/S0002-9939-2011-10897-9

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