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arXiv · 1711.10901

Finiteness of Log Minimal Models and Nef curves on $3$-folds in characteristic $p>5$

Omprokash Das
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Abstract

In this article we prove a finiteness result on the number of log minimal models for $3$-folds in 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 $X$.

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Omprokash Das. 2017-11-28. Finiteness of Log Minimal Models and Nef curves on $3$-folds in characteristic $p>5$. https://doi.org/10.1017/nmj.2018.28

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