Principal G-Bundles and Abelian Varieties: The Hitchin System

By Renata Scognamillo

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 H: T*M->K, 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.

• Format: Paperback
• Language: English
• ISBN: 8876422811
• ISBN13: 9788876422812
• Release Date: October 1998
• Publisher: Edizioni Della Normale
• Length: 49 Pages
• Weight: 0.32 lbs.
• Dimensions: 0.2" x 6.7" x 9.5"