Special rays in the Mori cone of a projective variety

Abstract

Let $X$ be a smooth $n$-dimensional projective variety over an algebraically closed field $k$ such that $K_X$ is not nef. We give a characterization of non nef extremal rays of $X$ of maximal length (i.e of length $n-1$); in the case of Char$(k) = 0$ we also characterize non nef rays of length $n-2$.