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$ F$-invariants of diagonal hypersurfaces


Author: Daniel J. Hernández
Journal: Proc. Amer. Math. Soc. 143 (2015), 87-104
MSC (2010): Primary 13A35
DOI: https://doi.org/10.1090/S0002-9939-2014-12260-X
Published electronically: September 9, 2014
MathSciNet review: 3272734
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Abstract: In this note, we derive formulas for the $ F$-pure threshold, higher jumping numbers, and test ideals of diagonal and Fermat hypersurfaces. For these hypersurfaces, we answer a question of Schwede regarding the denominators of $ F$-pure thresholds, and obtain tight upper bounds for the number of higher jumping numbers. Our results are valid over all (or all but finitely many) characteristics, and therefore allow us to construct examples in which the characteristic $ p$ setting is drastically different than that over $ \mathbb{C}$.


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Additional Information

Daniel J. Hernández
Affiliation: Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California 94720-5070
Email: daniel.j.hernandez1@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12260-X
Received by editor(s): September 25, 2012
Received by editor(s) in revised form: March 16, 2013
Published electronically: September 9, 2014
Additional Notes: The author was partially supported by the National Science Foundation RTG grant number 0502170 at the University of Michigan.
Communicated by: Irena Peeva
Article copyright: © Copyright 2014 Daniel J. Hernández

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