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arXiv · 1305.3502

On base point freeness in positive characteristic

Paolo Cascini·Hiromu Tanaka·Chenyang Xu
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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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Paolo Cascini, Hiromu Tanaka, Chenyang Xu. 2013-05-15. On base point freeness in positive characteristic. https://arxiv.org/abs/1305.3502

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