Basepoint freeness for big line bundles in positive characteristic, with applications to M_g and to 3-fold MMP
Abstract
Description
I give a necessary and sufficient condition for a nef and big line bundle in positive characteristic to be semi-ample, and then give two applications: I show that the relative dualizing sheaf of the universal curve is semi-ample, in positive characteristic, and give a simple example which shows that this, and the semi-ampleness criterion, fail in characteristic zero. My second application is to Mori's program for minimal models of 3-folds. I prove a version of the Basepoint Free Theorem (for big line bundles on 3-folds of positive characteristic) and a simple Cone Theorem, for 3-folds of positive Kodaira dimension.
I have corrected several errors from the original version, and simplified the proof of the contraction theorem. to appear in Annals of Math. arXiv admin note: see math.AG/9901149 for published version accidentally submitted anew in Annals migration
I have corrected several errors from the original version, and simplified the proof of the contraction theorem. to appear in Annals of Math. arXiv admin note: see math.AG/9901149 for published version accidentally submitted anew in Annals migration