A simply connected numerical Godeaux surface with ample canonical class

Abstract

We 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 typos