On base point freeness in positive characteristic
On base point freeness in positive characteristic
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DOI：
10.24033/asens.2269
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发表时间：
2013-05
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影响因子：
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通讯作者：
P. Cascini;Hiromu Tanaka;Chenyang Xu-
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文献类型：
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作者：
P. Cascini;Hiromu Tanaka;Chenyang Xu-
本文证明了：如果$（X，A+B）$是定义在正特征的代数闭域上的一对，使得$（X，B）$是强F$-正则的，$A$是充分的，$K_X+A+B$是严格nef的，则$K_X + A+B$是充分的.同样地，我们证明了对于一个对数对$（X，A+B）$，$A$是充分的，$B $是有效的，$K_X+A+B$是大的，如果它是nef的，并且有最大的nef维数。作为应用，我们建立了关于nef阈值的一个合理性定理和关于正特征的三维最小模型规划的各种结果。
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.