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Article Dans Une Revue Experimental Mathematics Année : 2023

DECOMPOSING JACOBIANS VIA GALOIS COVERS

Résumé

Let φ : X → Y be a (possibly ramied) cover between two algebraic curves of positive genus. We develop tools that may identify the Prym variety of φ, up to isogeny, as the Jacobian of a quotient curve C in the Galois closure of the composition of φ with a well-chosen map Y → P 1. This method allows us to recover all previously obtained descriptions of a Prym variety in terms of a Jacobian that are known to us, besides yielding new applications. We also nd algebraic equations for some of these new cases, including one where X has genus 3, Y has genus 1 and φ is a degree 3 map totally ramied over 2 points.
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hal-02512858 , version 1 (20-03-2020)

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Elisa Lorenzo García, Davide Lombardo, Christophe Ritzenthaler, Jeroen Sijsling. DECOMPOSING JACOBIANS VIA GALOIS COVERS. Experimental Mathematics, 2023, 32 (1), pp.218-240. ⟨10.1080/10586458.2021.1926008⟩. ⟨hal-02512858⟩
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