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Godeaux and Campedelli Surfaces via Deformations

Author

Listed:
  • Haseeb Wali

    (Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad 44000, Pakistan)

  • Sohail Iqbal

    (Department of Mathematics, COMSATS University Islamabad, Islamabad Campus, Islamabad 44000, Pakistan)

Abstract

In this paper, we construct two deformations of the Godeaux surface with π 1 ≅ Z 4 , 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.

Suggested Citation

  • Haseeb Wali & Sohail Iqbal, 2024. "Godeaux and Campedelli Surfaces via Deformations," Mathematics, MDPI, vol. 12(19), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:19:p:3123-:d:1493040
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    References listed on IDEAS

    as
    1. Sohail Iqbal, 2017. "Godeaux, Campedelli, and surfaces of general type with χ = 4 and 2 ≤ K 2 ≤ 8," Mathematische Nachrichten, Wiley Blackwell, vol. 290(14-15), pages 2296-2307, October.
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