On degenerations of Z=2-Godeaux surfaces

• Eduardo Dias ^[1] ; Carlos Rito ^[2] ; Giancarlo Urzúa ^[3]
  1. [1] Universidade Do Porto

     Universidade Do Porto

     Santo Ildefonso, Portugal

     
  2. [2] Universidade de Trás-os-Montes e Alto Douro

     Universidade de Trás-os-Montes e Alto Douro

     Vila Real (São Pedro), Portugal

     
  3. [3] Pontificia Universidad Católica de Chile

     Pontificia Universidad Católica de Chile

     Santiago, Chile

     

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• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 5, 2022, págs. 1399-1423
• Idioma: inglés
• DOI: 10.4171/RMI/1376
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• Resumen

  • We compute equations for the Coughlan’s family of Godeaux surfaces with torsion \mathbb{Z}/2Z/2, which we call \mathbb{Z}/2Z/2-Godeaux surfaces, and we show that it is (at most) 7 dimensional. We classify all non-rational KSBA degenerations WW of \mathbb{Z}/2Z/2-Godeaux surfaces with one Wahl singularity, showing that WW is birational to particular either Enriques surfaces, or D_{2,n}D2,n elliptic surfaces, with n = 3, 4n=3,4 or 66. We present examples for all possibilities in the first case, and for n = 3, 4n=3,4 in the second