  Let $E$ be an ample vector bundle of rank $r$ on a projective variety $X$
with only log-terminal singularities. We consider the nefness of adjoint
divisors $K_X+(t-r)det(E)$ when $t>=dim(X)$ and $t>r$. As a corollary, we
classify pairs $(X,E)$ with $c_r$-sectional genus zero.
