In this paper, we construct two deformations of the Godeaux surface with π1≅Z4, such that each central fibre contains a family of conics. We show that surfaces that are birational to these Godeaux surfaces exist in two connected components of the moduli space of the Campedelli surfaces with a fundamental group of order 8. The whole construction is simplified by the use of key varieties.
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Wali et al. (2024) studied this question.
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