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The complex geometry of an integrable system

Ahmed Lesfari (2003)

Archivum Mathematicum

In this paper, a finite dimensional algebraic completely integrable system is considered. We show that the intersection of levels of integrals completes into an abelian surface (a two dimensional complex algebraic torus) of polarization 2 , 8 and that the flow of the system can be linearized on it.

The geometry of Calogero-Moser systems

Jacques Hurtubise, Thomas Nevins (2005)

Annales de l’institut Fourier

We give a geometric construction of the phase space of the elliptic Calogero-Moser system for arbitrary root systems, as a space of Weyl invariant pairs (bundles, Higgs fields) on the r -th power of the elliptic curve, where r is the rank of the root system. The Poisson structure and the Hamiltonians of the integrable system are given natural constructions. We also exhibit a curious duality between the spectral varieties for the system associated to a root system, and the Lagrangian varieties for...

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