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

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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Submitted on : Wednesday, January 4, 2017 - 1:56:45 PM
Last modification on : Thursday, February 28, 2019 - 6:26:02 PM

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  • HAL Id : hal-01426349, version 1
  • ARXIV : 1612.07033

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Christophe Ritzenthaler, Matthieu Romagny. On the Prym variety of genus 3 covers of genus 1 curves. Épijournal de Géométrie Algébrique, EPIGA, 2018, 2, 8 pp. ⟨hal-01426349⟩

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