  We show that the Craighero-Gattazzo surface, the minimal resolution of an
explicit complex quintic surface with four elliptic singularities, is
simply-connected. This was conjectured by Dolgachev and Werner, who proved that
its fundamental group has a trivial profinite completion. The
Craighero-Gattazzo surface is the only explicit example of a smooth
simply-connected complex surface of geometric genus zero with ample canonical
class. We hope that our method will find other applications: to prove a
topological fact about a complex surface we use an algebraic reduction mod p
technique and deformation theory.
