论文标题
关于$ \ mathbb z/2 $ -Godeaux表面的退化
On degenerations of $\mathbb Z/2$-Godeaux surfaces
论文作者
论文摘要
我们计算Coughlan的Godeaux表面家族的方程式，并用Torsion $ \ Mathbb Z/2 $计算，我们称之为$ \ Mathbb Z/2 $ -Godeaux表面，我们表明它（最多）是7尺寸。我们将非理性的KSBA变性分类为$ \ mathbb z/2 $ -Godeaux表面，其中一个Wahl奇异性，表明$ w $对特定的Enriques表面或$ d_ {2，n} $ n = 3,4 $ n = 3,4 $或$ 6 $。我们介绍了第一种情况下所有可能性的示例，第二个情况下为$ n = 3,4 $。
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.
