Abstract
Let be a (possibly ramified) cover, with X and Y of strictly positive genus. We develop tools to identify the Prym variety of , up to isogeny, as the Jacobian of a quotient curve C of the Galois closure of a composition of with a well-chosen map that identifies branch points of . To our knowledge, this method recovers all previously obtained descriptions of Prym varieties as Jacobians. It also finds new decompositions, and for some of these, including one where X has genus 3, Y has genus 1 and is a degree 3 map totally ramified over 2 points, we find an algebraic equation of the curve C.
Acknowledgments
The fourth author was moreover supported by a Juniorprofessurenprogramm of the Science Ministry of Baden-Württemberg. Part of the work for this paper was carried out at the workshop “Arithmetic of Curves”, held in Baskerville Hall in August 2018. We would like to thank the organizers Alexander Betts, Tim Dokchitser, Vladimir Dokchitser, Céline Maistret and Beryl Stapleton, as well as the Baskerville Hall staff, for providing a great opportunity to concentrate on this project.
Declaration of Interest
No potential conflict of interest was reported by the author(s).