  Let $f:X\rightarrow Y$ be a generically smooth morphism between irreducible
smooth projective curves over an algebraically closed field of arbitrary
characteristic. We prove that the vector bundle $((f_*{\mathcal O}_X)/{\mathcal
O}_Y)^*$ is virtually globally generated. Moreover, $((f_*{\mathcal
O}_X)/{\mathcal O}_Y)^*$ is ample if and only if $f$ is genuinely ramified.
