2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/150267Mumford defined a natural isomorphism between the intermediate jacobian of a conic-bundle over $P^2$ and the Prym variety of a naturally defined étale double cover of the discrminant curve of the conic-bundle. Clemens and Griffiths used this isomorphism to give a proof of the irrationality of a smooth cubic threefold and Beauville later generalized the isomorphism to intermediate jacobians of odd-dimensional quadric-bundles over $P^2$. We further generalize the isomorphism to the primitive cohomology of a smooth cubic hypersurface in $P^n$.AMS-Latex, 39 pagesAlgebraic Geometry14J70 (Primary) 14J45 (Secondary)text