$F$-invariants of diagonal hypersurfaces
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- by Daniel J. Hernández
- Proc. Amer. Math. Soc. 143 (2015), 87-104
- DOI: https://doi.org/10.1090/S0002-9939-2014-12260-X
- Published electronically: September 9, 2014
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 $\mathbb {C}$.References
Bibliographic Information
- Daniel J. Hernández
- Affiliation: Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California 94720-5070
- Email: daniel.j.hernandez1@gmail.com
- 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
- © Copyright 2014 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
- MathSciNet review: 3272734