A theorem on the adjoint system for vector bundles

In this paper, we study the classification theory of uniruled varieties by means of the adjoint system for vector bundles on the varieties. We prove that ifE is an ample vector bundle on a smooth projective varietyX with rank(E)=dimX-2, thenK _X +C ₁ (E) is numerically effective except in a few cases. In all of the exceptional cases,X is a uniruled variety. As consequences, we generalized a result of Fujita Fu3] and Ionescu Io] and improve upon a theorem of Wiśniewski Wi1].