2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147137The purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2) to show that - on a Kähler surface - the solutions of the monopole equations can be interpreted as algebraic objects, namely effective divisors, 3) to give - as an application - a short selfcontained proof for the fact that rationality of complex surfaces is a ${\cal C}^{\infty}$-property.Duke preprint, LaTeXAlgebraic Geometrytext