1997/01/25 by Elham Izadi, E. Izadi, Izadi, E.
Mathematics · #14J70 (Primary) 14J45 (Secondary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #alg-geom #math.AG #msc:14J45 #msc:14J70
paper · pdf · doi:10.48550/arxiv.alg-geom/9701012
AMS-Latex, 39 pages
arxiv created 1997/01/25 · openalex publication_date 1997/01/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Mumford defined a natural isomorphism between the intermediate jacobian of a conic-bundle over P2 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 P2. We further generalize the isomorphism to the primitive cohomology of a smooth cubic hypersurface in Pn.