Godeaux and Campedelli Surfaces via Deformations

Haseeb Wali and Sohail Iqbal ()
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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

Mathematics, 2024, vol. 12, issue 19, 1-13

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.

Keywords: ?-Gorenstein smoothing; surfaces of general type; Tom & Jerry (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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