Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



$ F$-pure thresholds of binomial hypersurfaces

Author: Daniel J. Hernández
Journal: Proc. Amer. Math. Soc. 142 (2014), 2227-2242
MSC (2010): Primary 13A35, 13B25, 13P99, 14Q10
Published electronically: March 28, 2014
MathSciNet review: 3195749
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this article, we develop an algorithm that computes the $ F$-pure threshold of a binomial hypersurface over a field of characteristic $ p>0$. This algorithm is related to earlier work of Shibuta and Takagi (e.g., both depend on properties of certain associated rational polytopes), but differs in that it works in all characteristics.

References [Enhancements On Off] (What's this?)

  • [BMS08] Manuel Blickle, Mircea Mustaţa, and Karen E. Smith, Discreteness and rationality of $ F$-thresholds, Michigan Math. J. 57 (2008), 43-61. Special volume in honor of Melvin Hochster. MR 2492440 (2010c:13003),
  • [Her11] Daniel J. Hernández, $ F$-purity versus log canonicity for polynomials, preprint (2011). arXiv: 1112:2423
  • [Luc78] Edouard Lucas, Theorie des Fonctions Numeriques Simplement Periodiques, Amer. J. Math. (1878).
  • [MTW05] Mircea Mustaţa, Shunsuke Takagi, and Kei-ichi Watanabe, F-thresholds and Bernstein-Sato polynomials, European Congress of Mathematics, Eur. Math. Soc., Zürich, 2005, pp. 341-364. MR 2185754 (2007b:13010)
  • [ST09] Takafumi Shibuta and Shunsuke Takagi, Log canonical thresholds of binomial ideals, Manuscripta Math. 130 (2009), no. 1, 45-61. MR 2533766 (2010j:14031),
  • [TW04] Shunsuke Takagi and Kei-ichi Watanabe, On F-pure thresholds, J. Algebra 282 (2004), no. 1, 278-297. MR 2097584 (2006a:13010),

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 13A35, 13B25, 13P99, 14Q10

Retrieve articles in all journals with MSC (2010): 13A35, 13B25, 13P99, 14Q10

Additional Information

Daniel J. Hernández
Affiliation: Mathematical Sciences Research Institute, 17 Gauss Way, Berkeley, California 94720-5070
Address at time of publication: Department of Mathematics, The University of Utah, Salt Lake City, UT 84112

Received by editor(s): October 11, 2011
Received by editor(s) in revised form: July 13, 2012
Published electronically: March 28, 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

American Mathematical Society