Principal G-bundles And Abelian Varieties

In 1987, Hitchin applied the theory of spectral curves, considering the moduli space of stable principal G-bundles over a compact Riemann surface C and used spectral curves to describe the cotangent bundle T*M as an \'algebraically completely integrable Hamiltonian system\', defining an analytic map H:T*M->K, where K is a suitable vector space.