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.

翻译：我们给出了属2曲线Jacobian在P^3 × P^3中的嵌入显式方程，该方程提供了椭圆曲线Edwards曲线模型在阿贝尔曲面上的自然类比。与标准P^{15}中的版本相比，这极大简化了Jacobian簇的描述。同时我们给出了一个条件，在该条件下如同Edwards曲线一样，此类阿贝尔曲面具有泛群律。