On degenerations of -Godeaux surfaces
Eduardo Dias
Faculdade de Ciências da Universidade do Porto, PortugalCarlos Rito
Universidade de Trás-os-Montes e Alto Douro, Vila Real, PortugalGiancarlo Urzúa
Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
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Abstract
We compute equations for the Coughlan’s family of Godeaux surfaces with torsion , which we call -Godeaux surfaces, and we show that it is (at most) 7 dimensional. We classify all non-rational KSBA degenerations of -Godeaux surfaces with one Wahl singularity, showing that is birational to particular either Enriques surfaces, or elliptic surfaces, with or . We present examples for all possibilities in the first case, and for in the second.
Cite this article
Eduardo Dias, Carlos Rito, Giancarlo Urzúa, On degenerations of -Godeaux surfaces. Rev. Mat. Iberoam. 38 (2022), no. 5, pp. 1399–1423
DOI 10.4171/RMI/1376