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Birkhäuser - Birkhäuser Mathematics - Scuola Normale Superiore | Principal G-bundles and abelian varieties: the Hitchin system

Principal G-bundles and abelian varieties: the Hitchin system

Scognamillo, Renata

49 p.

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  • About this book

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.

Content Level » Research

Keywords » Hamiltonian systems - spectral curves

Related subjects » Scuola Normale Superiore

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