The linear flows in the space of Krichever-Lax matrices over an algebraic curve

Details The linear flows in the space of Krichever-Lax matrices over an algebraic curve The linear flows in the space of Krichever-Lax matrices over an algebraic curve

2008-01-14

arxiv.org/abs/0801.2012v1

Mathematics

Dynamical Systems

Scientific paper

In \cite{kri02}, I. M. Krichever invented the space of matrices parametrizing the cotangent bundle of moduli space of stable vector bundles over a compact Riemann surface, which is named as the Hitchin system after the investigation \cite{hit87}. We study a necessary and sufficient condition for the linearity of flows on the space of Krichever-Lax matrices in a Lax representation in terms of cohomological classes using the similar technique and analysis from the work \cite{grif85} by P. A. Griffiths.

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