Vol. 9, No. 3, 2015

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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
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