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)|
|Number of pages||34|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - Sep 1 2015|
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