Abstract
Mumford 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
.