Marked Godeaux surfaces with special bicanonical fibers

Abstract

In this paper we study marked numerical Godeaux surfaces with special bicanonical fibers. Based on the construction method of marked Godeaux surfaces in [12] we give a complete characterization for the existence of hyperelliptic bicanonical fibers and torsion fibers. Moreover, we describe how the families of Reid and Miyaoka with torsion $Z/3Z$ and $Z/5Z$ arise in our homological setting.