Papers › Decomposing Jacobians via Galois covers
Decomposing Jacobians via Galois covers
Davide Lombardo, Elisa Lorenzo García, Christophe Ritzenthaler, Jeroen Sijsling
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Let ϕ: X→Y be a (possibly ramified) 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→ℙ¹. 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 find 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 ramified over 2 points.
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