On degenerations of $\mathbb Z/2$-Godeaux surfaces

Eduardo Dias; Carlos Rito; Giancarlo Urzúa

On degenerations of $\mathbb Z/2$-Godeaux surfaces

Algebraic Geometry 2020-02-21 v1

Authors: Eduardo Dias , Carlos Rito , Giancarlo Urzúa

Abstract

We compute equations for Coughlan's family of Godeaux surfaces with torsion $\mathbb Z/2$ , which we call $\mathbb Z/2$ -Godeaux surfaces, and we show that it is (at most) 7 dimensional. We classify non-rational KSBA degenerations $W$ of $\mathbb Z/2$ -Godeaux surfaces with one Wahl singularity, showing that $W$ is birational to particular either Enriques surfaces, or $D_{2,n}$ elliptic surfaces, with $n=3,4$ or $6$ . We present examples for all possibilities in the first case, and for $n=3,4$ in the second.

Keywords

godeaux surfaces ksba degenerations wahl singularity enriques surfaces elliptic surfaces birational equivalence z/2-torsion

Cite

@article{arxiv.2002.08836,
  title  = {On degenerations of $\mathbb Z/2$-Godeaux surfaces},
  author = {Eduardo Dias and Carlos Rito and Giancarlo Urzúa},
  journal= {arXiv preprint arXiv:2002.08836},
  year   = {2020}
}

On degenerations of $\mathbb Z/2$-Godeaux surfaces

Abstract

Keywords

Cite

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