Geometric study of a family of integrable systems. (Étude géométrique d'une famille de systémes intégrables.)
Geometrische Untersuchung über die Bewegung eines starren Körpers. Von Carl Neumann in Leipzig
The complex geometry of an integrable system
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 and that the flow of the system can be linearized on it.
The geometry of Calogero-Moser systems
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 -th power of the elliptic curve, where 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...
Untersuchungen über die Bewegung eines Systemes starrer Körper