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Uniform bounds for strongly $ F$-regular surfaces


Authors: Paolo Cascini, Yoshinori Gongyo and Karl Schwede
Journal: Trans. Amer. Math. Soc. 368 (2016), 5547-5563
MSC (2010): Primary 14F18, 13A35, 14B05
DOI: https://doi.org/10.1090/tran/6515
Published electronically: October 7, 2015
MathSciNet review: 3458390
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Abstract: We show that if $ (X,B)$ is a two dimensional Kawamata log terminal pair defined over an algebraically closed field of characteristic $ p$, and $ p$ is sufficiently large, depending only on the coefficients of $ B$, then $ (X,B)$ is also strongly $ F$-regular.


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Additional Information

Paolo Cascini
Affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
Email: p.cascini@imperial.ac.uk

Yoshinori Gongyo
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan – and – Department of Mathematics, Imperial College London, 180 Queen’s Gate, London SW7 2AZ, United Kingdom
Email: gongyo@ms.u-tokyo.ac.jp, y.gongyo@imperial.ac.uk

Karl Schwede
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802
Address at time of publication: Department of Mathematics, University of Utah, 155 S 1400 E Room 233, Salt Lake City, Utah 84112
Email: schwede@math.psu.edu, schwede@math.utah.edu

DOI: https://doi.org/10.1090/tran/6515
Keywords: $F$-regular, $F$-pure, log terminal, log canonical
Received by editor(s): February 15, 2014
Received by editor(s) in revised form: July 10, 2014
Published electronically: October 7, 2015
Additional Notes: The first author was partially supported by EPSRC grant P28327
The second author was partially supported by the Grand-in-Aid for Research Activity Start-Up $♯$24840009 from JSPS and research expense from the JRF fund.
The third author was partially supported by the NSF grant DMS #1064485, NSF FRG grant DMS #1265261/1501102, NSF CAREER grant DMS #1252860/1501115 and a Sloan Fellowship.
Article copyright: © Copyright 2015 American Mathematical Society

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