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

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.