Abstract:
In this paper the author determines when the principally polarized Prymian
P(˜C,I) of a Beauville pair (˜C,I) 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 Ng−4 of principally polarized Abelian varieties of dimension g whose theta-divisors have singular locus of dimension ⩾g−4; 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.
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