A journey between two curves

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Abstract

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.

Original languageEnglish (US)
Article number043
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume3
DOIs
StatePublished - Jan 1 2007
Externally publishedYes

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Keywords

  • Hitchin system
  • Monopoles
  • Nahm equations
  • Seiberg-Witten theory

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology

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