Affine parts of abelian surfaces as complete intersection of three quartics

Abstract

We consider an integrable system in five unknowns having three quartics invariants. We show that the complex affine variety defined by putting these invariants equal to generic constants, completes into an abelian surface; the jacobian of a genus two hyperelliptic curve. This system is algebraic completely integrable and it can be integrated in genus two hyperelliptic functions.