The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs

Details The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs

1995-05-08

arxiv.org/abs/alg-geom/9505012v1

Mathematics

Algebraic Geometry

latex

Scientific paper

We introduce coupled Seiberg-Witten equations, and we prove, using a generalized vortex equation, that, for Kaehler surfaces, the moduli space of solutions of these equations can be identified with a moduli space of holomorphic stable pairs. In the rank 1 case, one recovers Witten's result identifying the space of irreducible monopoles with a moduli space of divisors. As application, we give a short proof of the fact that a rational surface cannot be diffeomorphic to a minimal surface of general type.

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