An 8-dimensional family of simply connected Godeaux surfaces

Abstract

In this paper we describe a construction method for numerical Godeaux surfaces based on homological algebra. We show the existence of an 8-dimensional locally complete family of simply connected numerical Godeaux surfaces.

arXiv comment28 pages. We have divided the previous version "Godeaux surfaces I" into two parts. This version describes the general construction method. The second part studies marked Godeaux surfaces with special bicanonical fibers