Effective Matsusaka’s theorem for surfaces in characteristic p

Di Cerbo, Gabriele; Fanelli, Andrea

doi:10.2140/ant.2015.9.1453

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Effective Matsusaka's theorem for surfaces in characteristic $p$

Gabriele Di Cerbo and Andrea Fanelli

Vol. 9 (2015), No. 6, 1453–1475

DOI: 10.2140/ant.2015.9.1453

Abstract

We obtain an effective version of Matsusaka’s theorem for arbitrary smooth algebraic surfaces in positive characteristic, which provides an effective bound on the multiple that makes an ample line bundle $D$ very ample. The proof for pathological surfaces is based on a Reider-type theorem. As a consequence, a Kawamata–Viehweg-type vanishing theorem is proved for arbitrary smooth algebraic surfaces in positive characteristic.

Keywords

effective Matsusaka, surfaces in positive characteristic, Fujita's conjectures, Bogomolov's stability, Reider's theorem, bend-and-break, effective Kawamata–Viehweg vanishing

Mathematical Subject Classification 2010

Primary: 14J25

Milestones

Received: 24 February 2015

Revised: 16 April 2015

Accepted: 17 May 2015

Published: 7 September 2015

Authors

Gabriele Di Cerbo
Department of Mathematics Columbia University New York, NY 10027 United States

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

Vol. 9, No. 6, 2015