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Fall and Winter 2016 On the behavior of singularities at the $F$-pure threshold
Eric Canton, Daniel J. Hernández, Karl Schwede, Emily E. Witt
Illinois J. Math. 60(3-4): 669-685 (Fall and Winter 2016). DOI: 10.1215/ijm/1506067286

Abstract

We provide a family of examples for which the $F$-pure threshold and the log canonical threshold of a polynomial are different, but such that the characteristic $p$ does not divide the denominator of the $F$-pure threshold (compare with an example of Mustaţă–Takagi–Watanabe). We then study the $F$-signature function in the case that either the $F$-pure threshold and log canonical threshold coincide, or that $p$ does not divide the denominator of the $F$-pure threshold. We show that the $F$-signature function behaves similarly in those two cases. Finally, we include an appendix that shows that the test ideal can still behave in surprising ways even when the $F$-pure threshold and log canonical threshold coincide.

Citation

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Eric Canton. Daniel J. Hernández. Karl Schwede. Emily E. Witt. "On the behavior of singularities at the $F$-pure threshold." Illinois J. Math. 60 (3-4) 669 - 685, Fall and Winter 2016. https://doi.org/10.1215/ijm/1506067286

Information

Received: 11 May 2016; Revised: 15 March 2017; Published: Fall and Winter 2016
First available in Project Euclid: 22 September 2017

zbMATH: 06790322
MathSciNet: MR3705442
Digital Object Identifier: 10.1215/ijm/1506067286

Subjects:
Primary: 13A35, 14B05, 14J17

Rights: Copyright © 2016 University of Illinois at Urbana-Champaign

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Vol.60 • No. 3-4 • Fall and Winter 2016
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