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The smooth invariance of the Kodaira dimension of a complex surface. (English) Zbl 0858.57023
A proof of the following theorem is outlined: A complex surface of general type cannot be diffeomorphic to a rational surface. This implies that any complex surface diffeomorphic to a rational surface is rational. On the other side, any two diffeomorphic complex surfaces have the same Kodaira dimension, which was conjectured by Van de Ven.

MSC:
57N13 Topology of the Euclidean \(4\)-space, \(4\)-manifolds (MSC2010)
32J15 Compact complex surfaces
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