Special subvarieties of Pryms

Given an etale double cover of smooth algebraic curves, there is an associated principally polarized abelian variety, called the Prym variety of the cover. By a construction of Welters and Beauville, a complete linear system on the base curve gives rise to a pair of subvarieties of the Prym, called special subvarieties. The aim of this talk is to discuss the question of when the special subvarieties of a given Prym are algebraically equivalent and provide some applications to the study of algebraic cycles on Pryms.