English

$\mathbb Z/2$-Godeaux surfaces

Algebraic Geometry 2026-04-29 v3

Abstract

We prove that the moduli space of numerical Godeaux surfaces with torsion group Z/2\mathbb{Z}/2 is irreducible and unirational of dimension 8. Moreover, we show that the topological fundamental group of these surfaces is also Z/2\mathbb{Z}/2. Our approach is based on the explicit construction of equations for all universal covers of numerical Godeaux surfaces with torsion group Z/2\mathbb{Z}/2.

Keywords

Cite

@article{arxiv.2009.12645,
  title  = {$\mathbb Z/2$-Godeaux surfaces},
  author = {Eduardo Dias and Carlos Rito},
  journal= {arXiv preprint arXiv:2009.12645},
  year   = {2026}
}

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Final version

R2 v1 2026-06-23T18:49:00.640Z