Journal of Geometry and Symmetry in Physics

Seiberg-Witten Equations and Pseudoholomorphic Curves

Armen Sergeev

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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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J. Geom. Symmetry Phys., Volume 5 (2006), 106-117.

First available in Project Euclid: 20 May 2017

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

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