Nef and semiample divisors on rational surfaces
arXiv:1104.4270
Abstract
In this paper we study smooth projective rational surfaces, defined over an algebraically closed field of any characteristic, with pseudo-effective anticanonical divisor. We provide a necessary and sufficient condition in order for any nef divisor to be semiample. We adopt our criterion to investigate Mori dream surfaces in the complex case.
15 pages, 2 figures. Revised version, to appear in "Torsors, étale homotopy and applications to rational points"