description: During the past 20 years spectral curves have proved to be a successful geometrical tool for studying a large number of Hamiltonian systems. 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 where K is a suitable vector space. In this work we provide an explicit description of the generic fibres of H in term of both generalized Prym varieties and Prym-Tjurin varieties in the Jacobian of suitable spectral curves.
language: English
title: Principal G-bundles and abelian varieties: the Hitchin system
titlecomplete: Principal G-bundles and abelian varieties: the Hitchin system (Publications of the Scuola Normale Superiore)
publisher: Edizioni della Normale