Geodesic
On the Prym variety of genus 3 covers of genus 1 curves
Épijournal de Géométrie Algébrique, Tome 2 (2018)

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Given a generic degree-2 cover of a genus 1 curve D by a non hyperelliptic genus 3 curve C over a field k of characteristic different from 2, we produce an explicit genus 2 curve X such that Jac(C) is isogenous to the product of Jac(D) and Jac(X). This construction can be seen as a degenerate case of a result by Nils Bruin. 
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     author = {Ritzenthaler, Christophe and Romagny, Matthieu},
     title = {On the {Prym} variety of genus 3 covers of genus 1 curves},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
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Ritzenthaler, Christophe; Romagny, Matthieu. On the Prym variety of genus 3 covers of genus 1 curves. Épijournal de Géométrie Algébrique, Tome 2 (2018). doi: 10.46298/epiga.2018.volume2.3663

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