The linear flows in the space of Krichever-Lax matrices over an algebraic curve
Abstract
In 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 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 grif85 by P. A. Griffiths.
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