2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144142In this paper we study the Brill-Noether theory of sub-line bundles of a general, stable rank-two vector bundle on a curve C with general moduli. We relate this theory to the geometry of unisecant curves on smooth, non-special scrolls with hyperplane sections isomorphic to C. Most of our results are based on degeneration techniques.16 pages, Latex2e, Submitted preprintAlgebraic Geometry14H60, 14H51, 14D06, 14C20 (Primary); 14J26, 14N10 (Secondary)text