Prym varieties: theory and applications

In this paper the author determines when the principally polarized Prymian $P(\widetilde C,I)$ of a Beauville pair $(\widetilde C,I)$ 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 $N_{g-4}$ of principally polarized Abelian varieties of dimension $g$ whose theta-divisors have singular locus of dimension $\geqslant g-4$; 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.
Bibliography: 32 titles.