LAUSR

Let φ : X → Y be a (possibly ramied) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of φ, up to isogeny, as the Jacobian of a quotient curve C in the Galois closure of the composition of φ with a well-chosen map Y → P 1. This method allows us to recover all previously obtained descriptions of a Prym variety in terms of a Jacobian that are known to us, besides yielding new applications. We also nd algebraic equations for some of these new cases, including one where X has genus 3, Y has genus 1 and φ is a degree 3 map totally ramied over 2 points.