A journey between two curves

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 - 2007
Externally publishedYes

Fingerprint

Curve
Seiberg-Witten Theory
Holomorphic Curve
Scattering Problems
Line Bundle
Integrable Systems
Gauge Theory
System of equations

Keywords

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

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology
  • Mathematical Physics

Cite this

A journey between two curves. / Cherkis, Sergey.

In: Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), Vol. 3, 043, 2007.

Research output: Contribution to journalArticle

@article{d115f03041a04566bed52566f128e38b,
title = "A journey between two curves",
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.",
keywords = "Hitchin system, Monopoles, Nahm equations, Seiberg-Witten theory",
author = "Sergey Cherkis",
year = "2007",
doi = "10.3842/SIGMA.2007.043",
language = "English (US)",
volume = "3",
journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",
issn = "1815-0659",
publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - A journey between two curves

AU - Cherkis, Sergey

PY - 2007

Y1 - 2007

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84889236898&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84889236898&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2007.043

DO - 10.3842/SIGMA.2007.043

M3 - Article

VL - 3

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SN - 1815-0659

M1 - 043

ER -