Geodesic
A Journey Between Two Curves
Symmetry, integrability and geometry: methods and applications, Tome 3 (2007) Cet article a éte moissonné depuis la source Math-Net.Ru

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A typical solution of an integrable system is described in terms of a holomorphic curve and a line bundle over it. The curve provides the action variables while the time evolution is a linear flow on the curve's Jacobian. Even though the system of Nahm equations is closely related to the Hitchin system, the curves appearing in these two cases have very different nature. The former can be described in terms of some classical scattering problem while the latter provides a solution to some Seiberg–Witten gauge theory. This note identifies the setup in which one can formulate the question of relating the two curves.
Keywords: Hitchin system; Nahm equations; monopoles; Seiberg–Witten theory. 
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Sergey A. Cherkis. A Journey Between Two Curves. Symmetry, integrability and geometry: methods and applications, Tome 3 (2007). http://geodesic.mathdoc.fr/item/SIGMA_2007_3_a42/

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