On Rosenhein-Göpel configurations and integrable systems

Abstract

We give a birational morphism between two types of genus 2 Jacobians in ℙ15. One of them is related to an Algebraic Completely Integrable System: the Geodesic Flow on SO(4), metric II (so termed after Adler and van Moerbeke). The other Jacobian is related to a linear system in |4Θ| with 12 base points coming from a Göpel tetrad of 4 translates of the Θ divisor. A correspondence is given on the base spaces so that the Poisson structure of the SO(4) system can be pulled back to the family of Göpel Jacobians.