We consider two classifications of real Kummer quartics. They use the Heisenberg invariance of Kummer quartics. The first divides the whole variety of real Kummer quartics into four classes according to the Heisenberg-invariance type and then subdivides each class into subclasses to obtain a deformation classification. This subdivision into subclasses is performed by means of the topological classification of the real parts of real Kummer quartics. The second classification deals with the set of real Kummer quartics with a fixed Heisenberg group. Such a set consists of a continuous part and a discrete part. We describe the deformation classes of the continuous part and describe its discrete part.

中文翻译：

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真正的Kummer四次方程及其海森堡不变性

我们考虑了真正的Kummer四次方的两种分类。他们使用Kummer四次方的Heisenberg不变性。首先根据海森堡不变类型将整个真实的Kummer四次方划分为四个类别，然后将每个类别细分为子类以获得变形分类。通过对真正的Kummer四次方的实部进行拓扑分类，可以将这些子类细分。第二类分类处理带有固定的Heisenberg群的一组真正的Kummer四次曲面。这样的集合由连续部分和离散部分组成。我们描述了连续零件的变形类别并描述了它的离散零件。