A journey between two curves

Sergey A. Cherkis

doi:10.3842/SIGMA.2007.043

A journey between two curves

Sergey A. Cherkis

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 language	English (US)
Article number	043
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	3
DOIs	https://doi.org/10.3842/SIGMA.2007.043
State	Published - 2007
Externally published	Yes

Keywords

Hitchin system
Monopoles
Nahm equations
Seiberg-Witten theory

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2007.043

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AU - Cherkis, Sergey A.

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AB - 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.

KW - Hitchin system

KW - Monopoles

KW - Nahm equations

KW - Seiberg-Witten theory

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A journey between two curves

Abstract

Keywords

ASJC Scopus subject areas

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