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

11/02/2022

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by   E. Victor Flynn, et al.

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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, with no exceptions.