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FINITENESS OF LOG MINIMAL MODELS AND NEF CURVES ON $3$-FOLDS IN CHARACTERISTIC $p>5$

Part of: Birational geometry

Published online by Cambridge University Press:  10 September 2018

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OMPROKASH DAS*
Affiliation:
Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Math Sciences Building 6363, USA email [email protected], [email protected]
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Abstract

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 $X$.

MSC classification

Primary: 14E30: Minimal model program (Mori theory, extremal rays) 14E05: Rational and birational maps 14E99: None of the above, but in this section
Type
Article
Information
Nagoya Mathematical Journal , Volume 239 , September 2020 , pp. 76 - 109
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Copyright
© 2018 Foundation Nagoya Mathematical Journal

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