2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78815Given a covering f: X \to Y of projective manifolds, we consider the vector bundle E on Y given as the dual of f_*(Ø_X) / Ø_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.LaTeX2e, 26 pagesAlgebraic Geometry14E20, 14J60text