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On base point freeness in positive characteristic

Authors
  • Cascini, Paolo
  • Tanaka, Hiromu
  • Xu, Chenyang
Type
Preprint
Publication Date
Mar 18, 2014
Submission Date
May 15, 2013
Identifiers
arXiv ID: 1305.3502
Source
arXiv
License
Yellow
External links

Abstract

We prove that if $(X,A+B)$ is a pair defined over an algebraically closed field of positive characteristic such that $(X,B)$ is strongly $F$-regular, $A$ is ample and $K_X+A+B$ is strictly nef, then $K_X+A+B$ is ample. Similarly, we prove that for a log pair $(X,A+B)$ with $A$ being ample and $B$ effective, $K_X+A+B$ is big if it is nef and of maximal nef dimension. As an application, we establish a rationality theorem for the nef threshold and various results towards the minimal model program in dimension three in positive characteristic.

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