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Seiberg-Witten invariants and the Van de Ven conjecture. (Les invariants de Seiberg-Witten et la conjecture de Van de Ven.) (French. Abridged English version) Zbl 0867.14013
The paper gives a new and elegantly simple proof of the fact that a complex surface which is diffeomorphic to a rational surface is itself rational (i.e., being rational is a property which depends only on the differential structure of the surface). The proof relies on the use of Seiberg-Witten invariants and their interpretation as it has been developed by the authors themselves in a previous paper. – As a consequence of this result, the Van de Ven conjecture follows; i.e. it is proved that the Kodaira dimension of a complex surface is an invariant which depends only on the differential structure of the surface.

MSC:
14J26 Rational and ruled surfaces
57R50 Differential topological aspects of diffeomorphisms
14M20 Rational and unirational varieties
57R55 Differentiable structures in differential topology
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