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arXiv · 1410.1138

Poisson surfaces and algebraically completely integrable systems

Indranil Biswas·Jacques Hurtubise
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Abstract

One can associate to many of the well known algebraically integrable systems of Jacobians (generalized Hitchin systems, Sklyanin) a ruled surface which encodes much of its geometry. If one looks at the classification of such surfaces, there is one case of a ruled surface that does not seem to be covered. This is the case of projective bundle associated to the first jet bundle of a topologically nontrivial line bundle. We give the integrable system corresponding to this surface; it turns out to be a deformation of the Hitchin system.

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Indranil Biswas, Jacques Hurtubise. 2014-10-05. Poisson surfaces and algebraically completely integrable systems. https://doi.org/10.1016/j.geomphys.2014.10.009

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