A simply connected numerical Godeaux surface with ample canonical class

1997/04/25 by Igor Dolgachev, C. Werner, Dolgachev, I. +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9704022

openalex publication_date 1997/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Bloch's conjecture on surfaces of general type with an involution

Related

• Numerical Godeaux surfaces with an involution
• An 8-dimensional family of simply connected Godeaux surfaces
• Gorenstein stable Godeaux surfaces
• On degenerations of \mathbb Z/2-Godeaux surfaces
• A rigid, not infinitesimally rigid surface with K ample