2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59686We study the birationality (onto its image) of the Abel-Prym morphism associated with a Prym-Tuyrin variety. We use such result to prove that Picard bundles over Prym varieties are simple and moreover they are stable when the Abel-Prym morphism is not birational. As a consequence we obtain that Picard bundles over moduli spaces of stable vector bundles with fixed determinant are simple. We prove that Picard bundles over moduli spaces of rank 2 vector bundles on curves of genus 2 bundles are stable.15 pages, Latex2e + amsart, xypic neededAlgebraic Geometry14J60 (Primary), 14D20, 14H60 (Secondary)text