On local geometry of finite multitype hypersurfaces

Martin Kolar

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.