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. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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

https://projecteuclid.org/download/pdf_1/euclid.tjm/1270041986

Ken-ichi Seimiya

Papers

Kobayashi-Hitchin Correspondence for Perturbed Seiberg-Witten Equations