Characteristic Classes and Integrable Systems. General Construction

Understand

We consider topologically non-trivial Higgs bundles over elliptic curves with marked points and construct corresponding integrable systems.

• In the case of one marked point we call them the modified Calogero-Moser systems (MCM systems).
• Their phase space has the same dimension as the phase space of the standard CM systems with spin, but less number of particles and greater number of spin variables.
• Topology of the holomorphic bundles are defined by their characteristic classes.