  Given a covering f: X \to Y of projective manifolds, we consider the vector
bundle E on Y given as the dual of f_*(\O_X) / \O_Y. This vector bundles often
has positivity properties, e.g. E is ample when Y is projective space by a
theorem of Lazarsfeld. In general however E will not be ample due to the
geometry of Y. We prove various results when E is spanned, nef or generically
nef, under some assumptions on the base Y.
