The Craighero-Gattazzo surface is simply-connected

Tuesday, March 7, 2017 -
4:30pm to 5:30pm
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 first conjectured by Dolgachev and Werner, who proved that its fundamental group has trivial profinite completion. This makes the Craighero-Gattazzo surface the only explicitly known example of a smooth simply-connected complex surface of geometric genus zero with ample canonical class. The proof utilizes an interesting technique: to prove a topological fact about a complex surface we use algebraic reduction mod p and deformation theory.
Julie Rana
University of Minnesota
Event Location: 
Fine Hall 322