2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/74416Let (M,E) be a generalized polarized manifold, i.e., a pair of an n-dimensional smooth projective variety and an ample vector bundle E of rank r on M. Let t be the nef value of a polarized manifold (M, det E), i.e., the minimum of the set of real numbers s such that K+s det E is nef; we have tr<= n+1 by Mori's theory. In this paper we classify the pairs (M,E) in the following two cases: (1) n-2<= tr and t >= 1; (2) n+1-tr< t <= 1.53 pagesAlgebraic Geometry14J60, 14N30 (Primary) 14J45, 14E30 (Secondary)text