Research demonstrates irreducibility and unirationality of numerical Godeaux surfaces, indicating significant properties of their structure.
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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Dias et al. (2026) studied this question.
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