Vector Bundles and Lax Equations on Algebraic Curves
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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.
KeywordsVector Bundle Riemann Surface Spectral Parameter Algebraic Curf Compact Riemann Surface
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