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April 29, 2026Journal of Algebra0 citationsOpen Access

Z / 2 -Godeaux surfaces

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EDEduardo DiasCRCarlos Rito

Key Points

  • This research aims to explore the properties of numerical Godeaux surfaces with a torsion group Z/2.
  • Constructed explicit equations for universal covers of Godeaux surfaces.
  • Analyzed the moduli space to determine irreducibility and unirationality.
  • Examined the topological fundamental group.
  • Established that the moduli space is irreducible and unirational with a dimension of 8.
  • Showed that the topological fundamental group of these surfaces is Z/2.

Abstract

We prove that the moduli space of numerical Godeaux surfaces with torsion group Z / 2 is irreducible and unirational of dimension 8. Moreover, we show that the topological fundamental group of these surfaces is also 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 .

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Cite This Study

Dias et al. (2026) studied this question.

synapsesocial.com/papers/69f1a08eedf4b4682480717dhttps://doi.org/10.1016/j.jalgebra.2026.04.035
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