The geometry of Calogero-Moser systems

We give a geometric construction of the phase space at the elliptic CalogeroMoser system for arbitrary root systems, aw 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 the integrable system associated to the dual root system. Finally, the construction is shown to reduce to an existing one for the An root system.