$F$-thresholds of hypersurfaces
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- by Manuel Blickle, Mircea Mustaţǎ and Karen E. Smith PDF
- Trans. Amer. Math. Soc. 361 (2009), 6549-6565 Request permission
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.References
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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 Mustaţǎ
- 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
- MR Author ID: 343614
- Email: kesmith@umich.edu
- 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)
- © Copyright 2009 American Mathematical Society
- 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
- MathSciNet review: 2538604