### Abstract

Beauville [A. Beauville, Jacobiennes des courbes spectrales et systèmes hamiltoniens complètement intégrables, Acta. Math. 164 (1990) 211-235] 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 [D. Mumford, Tata Lectures on Theta II, Birkhäuser, 1984]. 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 [P. Vanhaecke, Linearising two-dimensional integrable systems and the construction of action-angle variables, Math. Z. 211 (1992) 265-313; P. Vanhaecke, Integrable systems in the realm of algebraic geometry, in: Lecture Notes in Mathematics, vol. 1638, 2001].

Original language | English |
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Pages (from-to) | 815-831 |

Number of pages | 17 |

Journal | Journal of Geometry and Physics |

Volume | 57 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2007 Feb 1 |

### Keywords

- Completely integrable system
- Jacobian variety
- Mumford system
- Spectral curve

### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Geometry and Topology

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## Cite this

*Journal of Geometry and Physics*,

*57*(3), 815-831. https://doi.org/10.1016/j.geomphys.2006.06.004