We study an irreducible real-analytic germ of an n-dimensional variety in n dimensional complex space. Assuming that the variety is Segre nondegenerate we define an averaging operator that generalizes the Moser–Webster involution. This operator can be thought of as being the CR structure of the singularity, and using this operator we study the set of functions that are restrictions of holomorphic functions. We give a condition on the flattening of the singularity, that is realizing the singularity as a codimention one subvariety of a nonsingular Levi-flat hypersurface.

中文翻译：

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Segre非简并的完全实子变量

我们研究了n维复杂空间中n维变量的不可约实解析细菌。假设该变种是Segre非退化的，我们定义了一个平均算子，该算子对Moser–Webster对合进行了概括。可以将此运算符视为奇点的CR结构，并使用该运算符来研究作为全纯函数限制的函数集。我们给出了奇异性变平的条件，即将奇异性实现为非奇异的Levi-flat超曲面的一个子集的子集。