The Catlin multitype and biholomorphic equivalence of models

TL;DR

This paper introduces a new approach to the Catlin multitype invariant for smooth hypersurfaces in complex space, providing criteria for biholomorphic equivalence of models and an explicit algorithm for computation.

Contribution

It offers an alternative method to analyze the Catlin multitype, proves biholomorphic equivalence of models, and presents a finite algorithm for computing the multitype.

Findings

Biholomorphic equivalence of models established.

Explicit description of biholomorphisms provided.

Finite algorithm for multitype computation developed.

Abstract

We consider an alternative approach to a fundamental CR invariant - the Catlin multitype. It is applied to a general smooth hypersurface in $\mathbbC^{n+1}$, 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 a necessary step in understanding local biholomorphic equivalence of Levi degenerate hypersurfaces of finite Catlin multitype.