2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/96904After giving an explicit description of all the non vanishing Dolbeault cohomology groups of ample line bundles on grassmannians, I give two series of vanishing theorems for ample vector bundles on a smooth projective variety. They imply a part of a conjecture by Fulton and Lazarsfeld about the connectivity of some degeneracy loci.published in Documenta MatematicaAlgebraic Geometry14F17text