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

We give the explicit equations for a \({\textbf{P}}^3 \times {\textbf{P}}^3\) ${\mathbf{P}}^3\times {\mathbf{P}}^3$ 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  \({\textbf{P}}^{15}\) ${\mathbf{P}}^{15}$ . We also give a condition under which, as for the Edwards curve, the abelian surfaces have a universal group law.