-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

DOI:
https://doi.org/10.1090/S0002-9947-09-04719-9

Published electronically:
July 16, 2009

MathSciNet review:
2538604

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Abstract | References | Similar Articles | Additional Information

Abstract: We use the -module theoretic description of generalized test ideals to show that in any -finite regular ring the -thresholds of hypersurfaces are discrete and rational. Furthermore we show that any limit of -pure thresholds of principal ideals in bounded dimension is again an -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

Email:
manuel.blickle@uni-essen.de

**Mircea Mustata**

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

Email:
mmustata@umich.edu

**Karen E. Smith**

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

Email:
kesmith@umich.edu

DOI:
https://doi.org/10.1090/S0002-9947-09-04719-9

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