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DAS, OMPROKASH
Nagoya mathematical journal, 09/2020, Volume: 239Journal Article
In this article, we prove a finiteness result on the number of log minimal models for 3-folds in $\operatorname{char}p>5$ . We then use this result to prove a version of Batyrev’s conjecture on the structure of nef cone of curves on 3-folds in characteristic $p>5$ . We also give a proof of the same conjecture in full generality in characteristic 0. We further verify that the duality of movable curves and pseudo-effective divisors hold in arbitrary characteristic. We then give a criterion for the pseudo-effectiveness of the canonical divisor $K_{X}$ of a smooth projective variety in arbitrary characteristic in terms of the existence of a family of rational curves on $X$ .
