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Discreteness of $ F$-jumping numbers at isolated non- $ \mathbb{Q}$-Gorenstein points

Authors: Patrick Graf and Karl Schwede
Journal: Proc. Amer. Math. Soc. 146 (2018), 473-487
MSC (2010): Primary 13A35, 14F18
Published electronically: September 6, 2017
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Abstract: We show that the $ F$-jumping numbers of a pair $ (X, \mathfrak{a})$ in positive characteristic have no limit points whenever the symbolic Rees algebra of $ -K_X$ is finitely generated outside an isolated collection of points. We also give a characteristic zero version of this result, as well as a generalization of the Hartshorne-Speiser-Lyubeznik-Gabber stabilization theorem describing the non-$ F$-pure locus of a variety.

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Additional Information

Patrick Graf
Affiliation: Lehrstuhl für Mathematik I, Universität Bayreuth, 95440 Bayreuth, Germany

Karl Schwede
Affiliation: Department of Mathematics, The University of Utah, 155 S 1400 E Room 233, Salt Lake City, Utah 84112

Keywords: Test ideals, $F$-jumping numbers, $\mathbb{Q}$-Gorenstein, multiplier ideals
Received by editor(s): May 23, 2016
Received by editor(s) in revised form: March 10, 2017
Published electronically: September 6, 2017
Additional Notes: The first-named author was supported in part by the DFG grant “Zur Positivität in der komplexen Geometrie”
The second-named author was supported in part by the NSF grant DMS #1064485, NSF FRG Grant DMS #1501115, NSF CAREER Grant DMS #1501102
Communicated by: Irena Peeva
Article copyright: © Copyright 2017 American Mathematical Society

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