A simply connected numerical Godeaux surface with ample canonical class

TL;DR

This paper proves the simple connectivity of a recent numerical Godeaux surface construction, demonstrating it as a double plane with an ample canonical class and no (-2)-curves, marking a novel example in algebraic geometry.

Contribution

It establishes the simple connectivity of a specific numerical Godeaux surface and shows how to realize it as a double plane with an ample canonical class.

Findings

The surface is simply connected.

It contains no (-2)-curves.

It has an 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.