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arXiv · 1612.07033

On the Prym variety of genus 3 covers of genus 1 curves

Christophe Ritzenthaler·Matthieu Romagny
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Abstract

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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Christophe Ritzenthaler, Matthieu Romagny. 2016-12-21. On the Prym variety of genus 3 covers of genus 1 curves. https://doi.org/10.46298/epiga.2018.volume2.3663

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