On degenerations of -Godeaux surfaces

  • Eduardo Dias

    Faculdade de Ciências da Universidade do Porto, Portugal
  • Carlos Rito

    Universidade de Trás-os-Montes e Alto Douro, Vila Real, Portugal
  • Giancarlo Urzúa

    Pontificia Universidad Católica de Chile, Santiago de Chile, Chile
On degenerations of $\mathbb{Z}/2$-Godeaux surfaces cover
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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