Poisson surfaces and algebraically completely integrable systems
Algebraic Geometry
2015-06-23 v1 Symplectic Geometry
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.
Cite
@article{arxiv.1410.1138,
title = {Poisson surfaces and algebraically completely integrable systems},
author = {Indranil Biswas and Jacques Hurtubise},
journal= {arXiv preprint arXiv:1410.1138},
year = {2015}
}