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A Prym construction for the cohomology of a cubic hypersurface

E. Izadi
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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 $P^n$.

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E. Izadi. 1997-01-25. A Prym construction for the cohomology of a cubic hypersurface. https://arxiv.org/abs/alg-geom/9701012

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