On degenerations of \mathbb Z/2-Godeaux surfaces

2020/02/20 by Dias, Eduardo, Rito, Carlos, Urzúa, Giancarlo
#14J29 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.08836

Abstract

We compute equations for Coughlan's family of Godeaux surfaces with torsion \mathbb Z/2, which we call \mathbb Z/2-Godeaux surfaces, and we show that it is (at most) 7 dimensional. We classify non-rational KSBA degenerations W of \mathbb Z/2-Godeaux surfaces with one Wahl singularity, showing that W is birational to particular either Enriques surfaces, or D_2,n elliptic surfaces, with n=3,4 or 6. We present examples for all possibilities in the first case, and for n=3,4 in the second.

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