Resumen de On degenerations of Z=2-Godeaux surfaces

Eduardo Dias, Carlos Rito, Giancarlo Urzúa

• 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