Basepoint freeness for nef and big line bundles in positive characteristic
Algebraic Geometry
2016-09-07 v1
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.
Keywords
Cite
@article{arxiv.math/9901149,
title = {Basepoint freeness for nef and big line bundles in positive characteristic},
author = {Seán Keel},
journal= {arXiv preprint arXiv:math/9901149},
year = {2016}
}
Comments
34 pages, published version