ON THE BLOWUPS OF NUMERICAL GODEAUX SURFACES

We give a short proof of the following result: Let X be a complex surf ace of general type. If the canonical divisor of the minimal model of X has selfintersection = 1, then X is not diffeomorphic to a rational surface. Our proof is the natural extension of the argument given in [ 5] for the case when X is minimal. This argument also gives informatio n about the non-existence of certain smooth embeddings of a-spheres in X, if X has geometric genus zero.