Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles

@article{Donagi1996SpectralCA,
  title={Spectral curves, algebraically completely integrable Hamiltonian systems, and moduli of bundles},
  author={Ron Y. Donagi and Eyal Markman},
  journal={arXiv: Algebraic Geometry},
  year={1996},
  pages={1-119}
}
This is the expanded text of a series of CIME lectures. We present an algebro-geometric approach to integrable systems, starting with those which can be described in terms of spectral curves. The prototype is Hitchin's system on the cotangent bundle of the moduli space of stable bundles on a curve. A variant involving meromorphic Higgs bundles specializes to many familiar systems of mathematics and mechanics, such as the geodesic flow on an ellipsoid and the elliptic solitons. We then describe… 
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