2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61938We prove a Lefschetz hyperplane theorem for the determinantal loci of a morphism between two holomorphic vector bundles $E$ and $F$ over a complex manifold under the condition that $E^*\ox F$ is Griffiths $k$-positive. We apply this result to find some homotopy groups of the Brill-Noether loci for a generic curve.(one small mistake corrected)Differential GeometryAlgebraic Geometry32Q55; 14M12; 14H51text