A Prym construction for the cohomology of a cubic hypersurface

Details A Prym construction for the cohomology of a cubic hypersurface A Prym construction for the cohomology of a cubic hypersurface

1997-01-25

arxiv.org/abs/alg-geom/9701012v1

Mathematics

Algebraic Geometry

AMS-Latex, 39 pages

Scientific paper

Mumford defined a natural isomorphism between the intermediate jacobian of a conic-bundle over $P^2$ and the Prym variety of a naturally defined \'etale 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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