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Communications in Mathematical Physics

, Volume 229, Issue 2, pp 229–269 | Cite as

Vector Bundles and Lax Equations on Algebraic Curves

  • I. Krichever

Abstract:

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.

Keywords

Vector Bundle Riemann Surface Spectral Parameter Algebraic Curf Compact Riemann Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • I. Krichever
    • 1
  1. 1.Department of Mathematics, Columbia University, New York, NY 10027, USA.¶E-mail: krichev@math.columbia.eduUS

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