The moduli space of numerical Godeaux surfaces with torsion group Z/2 is irreducible and unirational of dimension 8 with fundamental group Z/2, proven via explicit construction of equations for all universal covers.
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$\mathbb Z/2$-Godeaux surfaces
The moduli space of numerical Godeaux surfaces with torsion group Z/2 is irreducible and unirational of dimension 8 with fundamental group Z/2, proven via explicit construction of equations for all universal covers.