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We describe alternate methods of solution for a model arising in the work of Seiberg and Witten on N = 2 supersymmetric Yang-Mills theory and provide a complete argument for the characterization put forth by Argyres, Faraggi, and Shapere of the curve .
We show that for every open Riemann surface with non-abelian fundamental group there is a multiple-valued function on such that the fiberwise convex hull of the graph of fails to contain the graph of a single-valued holomorphic function on .
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