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Vector field construction of Segre sets

Joel Merker
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Abstract

A CR generic real analytic CR manifold M carries two families of Segre varieties and conjugate Segre varieties. We observe in this article that their complexifications give rise to two families of foliations of the complexification of M which coincide with the flow foliations induced by the complexified CR (1,0) and (0,1) vector fields tangent to M. As an application, we derive a new proof of the characterization of finite type in terms of Segre sets.

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Joel Merker. 2000-10-24. Vector field construction of Segre sets. https://arxiv.org/abs/math/9901010

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