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arXiv · 2201.12065

Marked Godeaux surfaces with special bicanonical fibers

Frank-Olaf Schreyer·Isabel Stenger
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Abstract

In this paper we study marked numerical Godeaux surfaces with special bicanonical fibers. Based on our construction method of marked Godeaux surfaces 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 $\mathbb{Z}/3\mathbb{Z}$ and $\mathbb{Z}/5\mathbb{Z}$ arise in our homological setting.

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Frank-Olaf Schreyer, Isabel Stenger. 2022-01-28. Marked Godeaux surfaces with special bicanonical fibers. https://arxiv.org/abs/2201.12065

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