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2006 Seiberg-Witten Equations and Pseudoholomorphic Curves
Armen Sergeev
J. Geom. Symmetry Phys. 5: 106-117 (2006). DOI: 10.7546/jgsp-5-2006-106-117


We consider the Taubes correspondence between solutions of Seiberg-Witten equations on a compact four-dimensional symplectic manifold and pseudo-holomorphic curves. We start from Kähler surfaces, in which case there is a direct correspondence between solutions of Seiberg-Witten equations and holomorphic curves. The general Taubes correspondence for symplectic four-manifolds involves, in contrast with the Kähler case, a limiting procedure, called the scaling limit. Under this scaling limit solutions of Seiberg-Witten equations reduce to families of solutions of certain vortex equations in the normal bundle of the limiting pseudoholomorphic curve.


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Armen Sergeev. "Seiberg-Witten Equations and Pseudoholomorphic Curves." J. Geom. Symmetry Phys. 5 106 - 117, 2006.


Published: 2006
First available in Project Euclid: 20 May 2017

zbMATH: 1118.53029
MathSciNet: MR2269884
Digital Object Identifier: 10.7546/jgsp-5-2006-106-117

Rights: Copyright © 2006 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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