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arXiv · 2211.01450

An analog of the Edwards model for Jacobians of genus 2 curves

E. Victor Flynn·Kamal Khuri-Makdisi
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Abstract

We give the explicit equations for a P^3 x P^3 embedding of the Jacobian of a curve of genus 2, which gives a natural analog for abelian surfaces of the Edwards curve model of elliptic curves. This gives a much more succinct description of the Jacobian variety than the standard version in P^{15}. We also give a condition under which, as for the Edwards curve, the abelian surfaces have a universal group law.

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E. Victor Flynn, Kamal Khuri-Makdisi. 2022-11-02. An analog of the Edwards model for Jacobians of genus 2 curves. https://doi.org/10.1007/s40993-024-00518-5

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