Jacobian variety and Integrable system -- after Mumford, Beauville and Vanhaecke

Details Jacobian variety and Integrable system -- after Mumford, Beauville and Vanhaecke Jacobian variety and Integrable system -- after Mumford, Beauville and Vanhaecke

2005-12-12

arxiv.org/abs/math-ph/0512033v2

Physics

Mathematical Physics

21 pages. The previous version of this manuscript was entitled `Integrable Hamiltonian system on the Jacobian of a spectral cu

Scientific paper

Beauville introduced an integrable Hamiltonian system whose general level set is isomorphic to the complement of the theta divisor in the Jacobian of the spectral curve. This can be regarded as a generalization of the Mumford system. In this article, we construct a variant of Beauville's system whose general level set is isomorphic to the complement of the `intersection' of the translations of the theta divisor in the Jacobian. A suitable subsystem of our system can be regarded as a generalization of the even Mumford system introduced by Vanhaecke.

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