| Prym varieties are abelian varieties obtained from connected, etale double covers of curves. They were introduced by Mumford (1974) in connection with the study the intermediate Jacobian of a cubic threefold, and were later used by Beauville (1977) to extended Mumford's construction to the case of arbitrary fibrations in odd dimensional quadrics. In this talk, I will review these constructions, and then discuss a few recent projects building on this work. This will include degenerations of intermediate Jacobians, extensions of the Prym map, and the cohomology of fibrations in quadrics over the rational numbers. This is joint work with (in various combinations) S. Grushevsky, K. Hulek, R. Laza and J. Achter. |