Abstract. We construct normal forms for Levi degenerate hypersurfaces of finite type in C 2 . As one consequence, an explicit solution to the problem of local biholomorphic equivalence is obtained. Another consequence determines the dimension of the stability group of the hypersurface.

We consider an alternative approach to a fundamental CR invariant -the Catlin multitype. It is applied to a general smooth hypersurface in C n+1 , not necessarily pseudoconvex. Using this approach, we prove biholomorphic equivalence of models, and give an explicit description of biholomorphisms between different models. A constructive finite algorithm for computing the multitype is described. The results can be viewed as providing a necessary step in understanding local biholomorphic equivalence of Levi degenerate hypersurfaces of finite Catlin multitype.

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The first part of this paper gives a complete description of local automorphism groups for Levi degenerate hypersurfaces of finite type in C 2 . It is also proved that, with the exception of hypersurfaces of the form v = |z| k , local automorphisms are always determined by their 1-jets. Using this result, the second part describes special normal forms which by an additional normalization eliminate the nonlinear symmetries of the model and allows to decide effectively about local equivalence of two hypersurfaces given in this normal form.

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