Bøger af 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.

As explained in the introduction, this represents a useful and important viewpoint in algebraic geometry, especially concerning the theory of algebraic curves and their function fields. of geometrical or topological nature) are often indicated, also to provide motivations and intuition for many results.