BASEPOINT FREENESS FOR NEF AND BIG LINE BUNDLES IN POSITIVE CHARACTERISTIC, WITH APPLICATIONS TO Mg AND TO 3-FOLD MMP

Abstract

A general eventual freeness result is given for nef and big line bundles in positive characteristic. One application is to the geometry of the universal stable curve over Mg , specifically, the eventual freeness of the relative dualizing sheaf, in positive characteristic. An example is given which shows this fails 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. §

Cite this paper

@inproceedings{Keel1999BASEPOINTFF, title={BASEPOINT FREENESS FOR NEF AND BIG LINE BUNDLES IN POSITIVE CHARACTERISTIC, WITH APPLICATIONS TO Mg AND TO 3-FOLD MMP}, author={S. Keel}, year={1999} }