On base point freeness in positive characteristic

Paolo Cascini; Hiromu Tanaka; Chenyang Xu

doi:10.24033/asens.2269

On base point freeness in positive characteristic

Paolo Cascini, Hiromu Tanaka, Chenyang Xu

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34 Scopus citations

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 andKX+A+B is strictly nef, then KX +A+B is ample. Similarly, we prove that for a log pair (X;A+B) with A being ample and B effective,KX +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.

Original language	English (US)
Pages (from-to)	1239-1272
Number of pages	34
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	48
Issue number	5
DOIs	https://doi.org/10.24033/asens.2269
State	Published - Sep 1 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.24033/asens.2269

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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 andKX+A+B is strictly nef, then KX +A+B is ample. Similarly, we prove that for a log pair (X;A+B) with A being ample and B effective,KX +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.",

author = "Paolo Cascini and Hiromu Tanaka and Chenyang Xu",

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AU - Cascini, Paolo

AU - Tanaka, Hiromu

AU - Xu, Chenyang

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N2 - 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 andKX+A+B is strictly nef, then KX +A+B is ample. Similarly, we prove that for a log pair (X;A+B) with A being ample and B effective,KX +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.

AB - 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 andKX+A+B is strictly nef, then KX +A+B is ample. Similarly, we prove that for a log pair (X;A+B) with A being ample and B effective,KX +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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On base point freeness in positive characteristic

Abstract

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