2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150076On an arbitrary compact Riemann surface, necessary and sufficient conditions are found for the existence of semistable vector bundles with slope between zero and one and a prescribed number of linearly independent holomorphic sections. Existence is achieved by minimizing the Yang-Mills-Higgs functional.LaTeX 2e (amsart)Algebraic Geometrytext