1.1 What is known as the Hitchin system is a completely integrable hamiltonian system (CIHS) involving vector bundles over algebraic curves, identified by Hitchin in ([H1], [H2]). It was recently generalized by Faltings [F]. In this paper we only consider the case of ranktwo vector bundles with trivial determinant. In that case the Hitchin system corresponding to a curve C of genus g is obtained as follows. Let
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Geemen et al. (1996) studied this question.
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