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Basepoint freeness for nef and big line bundles in positive characteristic

Seán Keel
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Abstract

A necessary and sufficient condition is given for semi-ampleness of a numerically effective (nef) and big line bundle in positive characteristic. One application is to the geometry of the universal stable curve over M_g, specifically, the semi-ampleness of the relative dualizing sheaf, in positive characteristic. An example is given which shows this and the semi-ampleness criterion fail in characteristic zero. A second application is to Mori's program for minimal models of 3-folds in positive characteristic, namely, to the existence of birational extremal contractions.

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Seán Keel. 1999-01-01. Basepoint freeness for nef and big line bundles in positive characteristic. https://arxiv.org/abs/math/9901149

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