The Catlin Multitype and Biholomorphic Equivalence of Models

Abstract

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.