Semiample vector bundles and a characterization of étale trivial vector bundles

Abstract

We prove that a vector bundle $E$ over a smooth complex projective variety $M$ is étale trivial if and only if $E$ is semiample and $c_1(E)\in H^2(M,\mathbb{Q})$ vanishes. Also, a vector bundle $E$ over a smooth complex projective curve is semiample if and only if it is virtually globally generated.

Final version