We introduce Kummer surfaces X=Km(CxC) with the group scheme G=mu_2 acting on the self-product of the rational cuspidal curve in characteristic two. The resulting quotients are normal surfaces having a configuration of sixteen rational double points of type A_1, together with a rational double point of type D_4. We show that our Kummer surfaces are precisely the supersingular K3 surfaces with Artin invariant sigma\leq 3, and characterize them by the existence of a certain configuration of thirty curves. After contracting suitable curves, they also appear as normal K3-like coverings for simply-connected Enriques surfaces.

中文翻译：

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与组方案相关的库默曲面

我们引入 Kummer 曲面 X=Km(CxC)，群方案 G=mu_2 作用于特征二中的有理尖峰曲线的自积。所得商是具有 16 个类型 A_​​1 的有理双点以及类型 D_4 的有理双点的配置的法向曲面。我们证明我们的 Kummer 曲面正是具有 Artin 不变 sigma\leq 3 的超奇异 K3 曲面，并通过存在 30 条曲线的特定配置来表征它们。在收缩合适的曲线后，它们也表现为简单连接的 Enriques 曲面的正常 K3 类覆盖物。