The classification of double planes of general type with K2=8 and pg=0

We study minimal double planes of general type with K-2 = 8 and p(g) = 0, namely pairs (S, sigma), where S is a minimal complex algebraic surface of general type with K-2 = 8 and p(g) = 0, and sigma is an automorphism of S of order 2 such that the quotient S/sigma is a rational surface. We prove that S is a free quotient (F x C)/G, where C is a curve, F is an hyperelliptic curve, G is a finite group that acts faithfully on F and C, and sigma is induced by the automorphisin tau x Id of F x C, tau being the hyperelliptic involution of F. We describe all the F, C, and G that occur in this way we obtain 5 families of surfaces with P-g = 0 and K-2 = 8, of which we believe only one was previously known. Using our classification we are able to give an alternative description of these surfaces as double covers of the plane, thus recovering a construction proposed by Du Val. In addition, we study the geometry of the subset of the moduli space of surfaces of general type with p(g) = 0 and K-2 = 8 that admit a double plane structure. (C) 2002 Elsevier Science (USA). All rights reserved.