On Rosenhain–Göpel Configurations and Integrable Systems

    2011, Volume 16, Numbers 3-4, pp.  210-222

    Author(s): Piovan L. A.

    We give a birational morphism between two types of genus 2 Jacobians in $\mathbb{P}^{15}$. 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 $|4\Theta|$ with 12 base points coming from a Göpel tetrad of 4 translates of the $\Theta$ 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.
    Keywords: integrable systems
    Citation: Piovan L. A., On Rosenhain–Göpel Configurations and Integrable Systems, Regular and Chaotic Dynamics, 2011, Volume 16, Numbers 3-4, pp. 210-222

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