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Mathematische Zeitschrift

, Volume 287, Issue 3–4, pp 1343–1353 | Cite as

On the base point free theorem and Mori dream spaces for log canonical threefolds over the algebraic closure of a finite field

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Abstract

The authors and D. Martinelli proved in (Algebra Number Theory 9(3):725–747, 2015) the base point free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field. In this paper, we drop the bigness condition when the characteristic is larger than five. Additionally, we discuss Mori dream spaces defined over the algebraic closure of a finite field.

Keywords

Base point free theorem Semiample line bundles Positive characteristic Finite fields 

Mathematics Subject Classification

Primary 14E30 Secondary 14C20 

Notes

Acknowledgements

We would like to thank Paolo Cascini, Yoshinori Gongyo, Yujiro Kawamata, Diletta Martinelli, Keiji Oguiso, Hiromu Tanaka and Joe Waldron for useful comments and suggestions. We would also like to thank the referee for carefully reading our manuscript and suggesting several improvements. The first author is supported by the Grant-in-Aid for Scientific Research (KAKENHI No. 25-3003). The second author is funded by EPSRC.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Graduate School of Mathematical SciencesThe University of TokyoMeguro-kuJapan
  2. 2.Department of MathematicsImperial College, LondonLondonUK

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