The coupled Seiberg-Witten equations, vortices and moduli spaces of stable pairs

Andrei Teleman (1) , Christian Okonek (1)

1 Institut für Mathematik [Zürich]

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.

Mots clés: Seiberg-Witten equations; non-abelian monopoles

Domaines: Géométrie différentielle [math.DG]; Géométrie algébrique [math.AG]

Andrei Teleman, Christian Okonek. The coupled Seiberg-Witten equations, vortices and moduli spaces of stable pairs. International Journal of Mathematics, 1995, 6 (6), pp.893-910. ⟨10.1142/S0129167X95000390⟩. ⟨hal-00881774⟩