Witten triples and the Seiberg-Witten equations on a complex surface

摘要

We study the solutions of the Seiberg-Witten equations on complex surfaces. We show that for a large class of parameters, the gauge equivalence classes of irreducible solutions of the twisted Seiberg-Witten equations correspond to stable Witten triples. We prove that on Kahler surfaces this correspondence is the set-theoretical support of an isomorphism of real-analytic spaces. This makes it possible to take multiplicities into account and generalizes and unifies results previously obtained by Witten.