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

1995/05/08 by Ch. Okonek, Okonek, Ch., Andrei Teleman +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9505012

openalex publication_date 1995/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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