  The purpose of this paper is: 1) to explain the Seiberg-Witten invariants, 2)
to show that - on a K\"ahler 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.
