Seiberg-Witten Invariants and Rationality of Complex Surfaces

Mathematics – Algebraic Geometry

Scientific paper

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Duke preprint, LaTeX

Scientific paper

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.

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