On the basepoint-free theorem for log canonical threefolds over the algebraic closure of a finite field

Martinelli, Diletta; Nakamura, Yusuke; Witaszek, Jakub

doi:10.2140/ant.2015.9.725

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On the basepoint-free theorem for log canonical threefolds over the algebraic closure of a finite field

Diletta Martinelli, Yusuke Nakamura and Jakub Witaszek

Vol. 9 (2015), No. 3, 725–747

DOI: 10.2140/ant.2015.9.725

Abstract

We prove the basepoint-free theorem for big line bundles on a three-dimensional log canonical projective pair defined over the algebraic closure of a finite field. This theorem is not valid for any other algebraically closed field.

Keywords

basepoint-free theorem, semiample line bundles, positive characteristic, finite fields

Mathematical Subject Classification 2010

Primary: 14E30

Secondary: 14C20

Milestones

Received: 2 September 2014

Revised: 11 January 2015

Accepted: 16 February 2015

Published: 17 April 2015

Authors

Diletta Martinelli
Department of Mathematics Imperial College London 180 Queen’s Gate London SW7 2AZ United Kingdom

Yusuke Nakamura
Graduate School of Mathematical Sciences The University of Tokyo 3-8-1 Komaba, Meguro-ku Tokyo 153-8914 Japan

Jakub Witaszek
The London School of Geometry and Number Theory, Department of Mathematics University College London Gower Street London WC1E 6BT United Kingdom

Vol. 9, No. 3, 2015