Vector bundles and Lax equations on algebraic curves. (English) Zbl 1073.14048
Summary: The Hamiltonian theory of zero-curvature equations with spectral parameter on an arbitrary compact Riemann surface is constructed. It is shown that the equations can be seen as commuting flows of an infinite-dimensional field generalization of the Hitchin system. The field analog of the elliptic Calogero-Moser system is proposed. An explicit parameterization of Hitchin system based on the Tyurin parameters for stable holomorphic vector bundles on algebraic curves is obtained.
MSC:
14H70 | Relationships between algebraic curves and integrable systems |
14H60 | Vector bundles on curves and their moduli |
33E05 | Elliptic functions and integrals |
37J35 | Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests |
37K20 | Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions |
81R12 | Groups and algebras in quantum theory and relations with integrable systems |