On the base point free theorem for klt threefolds in large characteristic

Abstract

In this article we present a refinement of the base point free theorem for threefolds in positive characteristic. If $L$ is a nef Cartier divisor of numerical dimension at least one on a projective Kawamata log terminal threefold $(X,\Delta )$ over a perfect field $k$ of characteristic $p\gg 0$ such that $L-(K_X+\Delta )$ is big and nef, then we show that the linear system $|mL|$ is base point free for all sufficiently large integer $m>0$.

19 pages, v2: minor revision. To appear in Ann. Sci. Sc. Norm. Sup. Pisa