2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/148423We prove that a recent construction of a numerical Godeaux surface due to P. Craighero and R. Gattazzo is simply connected, and show how to realize their construction as a double plane. By proving that the surface contains no (-2)-curves, we obtain that this is the first example of a simply connected surface with vanishing geometric genus and ample canonical class.plain Tex 22 pages; 1 figure added, revised proofs of several results, corrected typosAlgebraic Geometrytext