$\mathbb Z/2$-Godeaux surfaces

Eduardo Dias; Carlos Rito

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arXiv · 2009.12645

$\mathbb Z/2$-Godeaux surfaces

Eduardo Dias·Carlos Rito

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Abstract

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

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Eduardo Dias, Carlos Rito. 2020-09-26. $\mathbb Z/2$-Godeaux surfaces. https://arxiv.org/abs/2009.12645

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