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$ F$-thresholds of hypersurfaces

Authors: Manuel Blickle, Mircea Mustata and Karen E. Smith
Journal: Trans. Amer. Math. Soc. 361 (2009), 6549-6565
MSC (2000): Primary 13A35; Secondary 14B05
Published electronically: July 16, 2009
MathSciNet review: 2538604
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Abstract: We use the $ D$-module theoretic description of generalized test ideals to show that in any $ F$-finite regular ring the $ F$-thresholds of hypersurfaces are discrete and rational. Furthermore we show that any limit of $ F$-pure thresholds of principal ideals in bounded dimension is again an $ F$-pure threshold; hence in particular the limit is rational.

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Additional Information

Manuel Blickle
Affiliation: Fachbereich Mathematik, Universität Duisburg-Essen, Standort Essen, 45117 Essen, Germany

Mircea Mustata
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Karen E. Smith
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109

Keywords: $F$-thresholds, test ideals, $F$-modules, nonstandard extension
Received by editor(s): July 23, 2007
Received by editor(s) in revised form: January 2, 2008
Published electronically: July 16, 2009
Additional Notes: Partial support was provided by grant SFB/TR 45 of the DFG (first author), NSF grants DMS-0758454, DMS 0111298 and a Packard Fellowship (second author), and NSF grant DMS-0500823(third author)
Article copyright: © Copyright 2009 American Mathematical Society

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