Abstract
In this paper the author determines when the principally polarized Prymian of a Beauville pair satisfying a certain stability type condition is isomorphic to the Jacobian of a nonsingular curve. As an application, he points out new components in the Andreotti-Mayer variety of principally polarized abelian varieties of dimension whose theta-divisors have singular locus of dimension ; he also proves a rationality criterion for conic bundles over a minimal rational surface in terms of the intermediate Jacobian. The first part of the paper contains the necessary preliminary material introducing the reader to the modern theory of Prym varieties.Figures: 10. Bibliography: 32 titles.
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