Marked Godeaux surfaces with special bicanonical fibers

Frank-Olaf Schreyer; Isabel Stenger

Marked Godeaux surfaces with special bicanonical fibers

Algebraic Geometry 2022-01-31 v1

Authors: Frank-Olaf Schreyer , Isabel Stenger

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.

Keywords

marked Godeaux surfaces numerical Godeaux surfaces bicanonical fibers hyperelliptic fibers torsion fibers homological setting Reid family Miyaoka family

Cite

@article{arxiv.2201.12065,
  title  = {Marked Godeaux surfaces with special bicanonical fibers},
  author = {Frank-Olaf Schreyer and Isabel Stenger},
  journal= {arXiv preprint arXiv:2201.12065},
  year   = {2022}
}

Comments

26 pages. The content of this paper was part of the original paper on arXiv:2009.05357 which we have divided into two parts

Marked Godeaux surfaces with special bicanonical fibers

Abstract

Keywords

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