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On local geometry of finite multitype hypersurfaces. (English) Zbl 1199.32042

Summary: This paper studies local geometry of hypersurfaces of finite multitype. Catlin’s definition of multitype is applied to a general smooth hypersurface in \(\mathbb C^{n+1}\). We prove biholomorphic equivalence of models in dimension three and describe all biholomorphisms between such models. A finite constructive algorithm for computing multitype is described. Analogous results for decoupled hypersurfaces are given.

MSC:

32V15 CR manifolds as boundaries of domains
32V35 Finite-type conditions on CR manifolds
32V40 Real submanifolds in complex manifolds
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