Godeaux and Campedelli Surfaces via Deformations

Abstract

In this paper, we construct two deformations of the Godeaux surface with π1≅Z4, such that each central fibre contains a family of conics. We show that surfaces that are birational to these Godeaux surfaces exist in two connected components of the moduli space of the Campedelli surfaces with a fundamental group of order 8. The whole construction is simplified by the use of key varieties.

Keywords

• ℚ-Gorenstein smoothing
• surfaces of general type
• Tom & Jerry