Basepoint freeness for nef and big line bundles in positive characteristic. (English) Zbl 0954.14004

Summary: 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 \(\overline M_g\), specifically, 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.


14C20 Divisors, linear systems, invertible sheaves
14H30 Coverings of curves, fundamental group
14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14G15 Finite ground fields in algebraic geometry
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