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On local geometry of finite multitype hypersurfaces

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Martin Kolar
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** Address.**
Institut of Mathematics and Statistics, Masaryk University

Janackovo nam. 2a, 602 00 Brno, Czech Republic

** E-mail:**
mkolar@math.muni.cz

**Abstract.**
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.

**AMSclassification. ** 32V15, 32V35, 32V40.

**Keywords. ** Finite type, Catlin's multitype, model hypersurfaces,
biholomorphic equivalence, decoupled domains.