Vector field construction of Segre sets

Joel Merker (1)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités

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.

Domaines: Variables complexes [math.CV]

Joel Merker. Vector field construction of Segre sets. 1998. ⟨hal-00003411⟩