Abstract
Suppose that X is a projective variety over an algebraically closed field of characteristic p > 0. Further suppose that L is an ample (or more generally in some sense positive) divisor. We study a natural linear system in
Funding source: NSF
Award Identifier / Grant number: postdoctoral fellowship #0703505
Funding source: Sloan Fellowship
Funding source: NSF
Award Identifier / Grant number: DMS #1064485
The author would like to thank Manuel Blickle, Hélène Esnault, Christopher Hacon, Mircea Mustaţă, Karen Smith, Kevin Tucker and Wenliang Zhang for inspiring conversations. The author would like to thank the referee, Christopher Hacon, Zsolt Patakfalvi and Kevin Tucker for numerous helpful comments on previous drafts of this paper. He is also very thankful to Brian Harbourne for pointing out some additional references in characteristic p > 0 related to Theorem 4.9. He is also thankful to Shunsuke Takagi and Nobuo Hara for some discussion of the history of the simple proof of special cases of Fujita's conjecture in characteristic p > 0. Large parts of this paper were written while visiting the Johannes Gutenberg-Universität Mainz during the summer of 2011. This visit was partially funded by the SFB/TRR45 Periods, moduli, and the arithmetic of algebraic varieties.
© 2014 by De Gruyter
