A simply connected numerical Campedelli surface with an involution

ABSTRACT. We construct a simply connected minimal complex surface of general type with pg = 0 and K2 = 2 which has an involution such that the minimal resolution of the quotient by the involution is a simply connected minimal complex surface of general type with pg = 0 and K2 = 1. In order to construct the example, we combine a double covering and Q-Gorenstein deformation. Especially, we develop a method for proving unobstruct-edness for deformations of a singular surface by generalizing a result of Burns and Wahl which characterizes the space of first order deformations of a singular surface with only rational double points. We describe the stable model in the sense of Kollár and Shepherd-Barron of the singular surfaces used for constructing the example. We count the dimension of the invariant part of the deformation space of the example under the induced Z/2Z-action. 1