Christophe Ritzenthaler ; Matthieu Romagny - 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: Christophe Ritzenthaler ; Matthieu Romagny

    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.

    Volume: Volume 2
    Published on: March 29, 2018
    Accepted on: March 9, 2018
    Submitted on: May 18, 2017
    Keywords: Mathematics - Algebraic Geometry,Mathematics - Number Theory,14Q05

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    Source : ScholeXplorer IsRelatedTo DOI 10.1006/jnth.1997.2105
    • 10.1006/jnth.1997.2105
    The Existence of Curves of Genus Two with Elliptic Differentials

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