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

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.

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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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Correspondence to Jakub Witaszek.

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Nakamura, Y., Witaszek, J. On the base point free theorem and Mori dream spaces for log canonical threefolds over the algebraic closure of a finite field. Math. Z. 287, 1343–1353 (2017). https://doi.org/10.1007/s00209-017-1871-6

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  • DOI: https://doi.org/10.1007/s00209-017-1871-6

Keywords

  • Base point free theorem
  • Semiample line bundles
  • Positive characteristic
  • Finite fields

Mathematics Subject Classification

  • Primary 14E30
  • Secondary 14C20