Geodesic
On local geometry of finite multitype hypersurfaces
Archivum mathematicum, Tome 43 (2007) no. 5, pp. 459-466.

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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.
Classification : 32V15, 32V35, 32V40, 32Vxx
Keywords: finite type; Catlin’s multitype; model hypersurfaces; biholomorphic equivalence; decoupled domains 
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     author = {Kol\'a\v{r}, Martin},
     title = {On local geometry of finite multitype hypersurfaces},
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     pages = {459--466},
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Kolář, Martin. On local geometry of finite multitype hypersurfaces. Archivum mathematicum, Tome 43 (2007) no. 5, pp. 459-466. http://geodesic.mathdoc.fr/item/ARM_2007__43_5_a9/