Abstract :
We study minimal double planes of general type with K2=8 and pg=0, namely pairs (S,σ), where S is a minimal complex algebraic surface of general type with K2=8 and pg=0, and σ is an automorphism of S of order 2 such that the quotient S/σ is a rational surface. We prove that S is a free quotient (F×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 σ is induced by the automorphism τ×Id of F×C, τ 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 pg=0 and K2=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 pg=0 and K2=8 that admit a double plane structure.
