Ritzenthaler, Christophe and Romagny, Matthieu - On the Prym variety of genus 3 covers of genus 1 curves

epiga:3663 - Épijournal de Géométrie Algébrique, March 29, 2018, Volume 2
On the Prym variety of genus 3 covers of genus 1 curves

Authors: Ritzenthaler, Christophe and Romagny, Matthieu

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.

Source : oai:arXiv.org:1612.07033
Volume: Volume 2
Published on: March 29, 2018
Submitted on: May 18, 2017
Keywords: Mathematics - Algebraic Geometry,Mathematics - Number Theory,14Q05


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