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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