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The Catlin Multitype and Biholomorphic Equivalence of Models

2010; Oxford University Press; Volume: 2010; Issue: 18 Linguagem: Inglês

10.1093/imrn/rnq013

1687-0247

Martin Kolář,

Advanced Algebra and Geometry

The paper introduces an alternative approach to a fundamental C-R 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 in C^n+1.