Godeaux and Campedelli Surfaces via Deformations

Godeaux and Campedelli Surfaces via Deformations

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 fundam...

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Veröffentlicht in:Mathematics (Basel) 2024-10, Vol.12 (19), p.3123
Hauptverfasser: Wali, Haseeb, Iqbal, Sohail
Format: Artikel
Sprache:eng
Schlagworte:
Conic sections
Conics
Deformation
Graphs
Mathematical research
surfaces of general type
Surfaces, Deformation of
Tom & Jerry
ℚ-Gorenstein smoothing
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Zusammenfassung: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12193123