Principal G-Bundles and Abelian Varieties: The Hitchin System
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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"
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