Classification of polynomial models without 2-jet determination in $\mathbb{C}^3$

TL;DR

This paper studies polynomial models of Levi-degenerate hypersurfaces in complex three-space, focusing on those lacking 2-jet determination, and provides a complete characterization of their symmetry structures.

Contribution

It offers a complete classification of Levi-degenerate polynomial models in ^3 without 2-jet determination, including explicit symmetry algebra descriptions.

Findings

Identifies models with nontrivial infinitesimal symmetries and vanishing 2-jets.

Provides explicit descriptions of the symmetry algebras for these models.

Characterizes all such models within the finite Catlin multitype setting.

Abstract

An intriguing phenomenon regarding Levi-degenerate hypersurfaces is the existence of nontrivial infinitesimal symmetries with vanishing 2-jets at a point. In this work we consider polynomial models of Levi-degenerate real hypersurfaces in $\mathbb{C}^3$ of finite Catlin multitype. Exploiting the structure of the corresponding Lie algebra, we characterize completely models without 2-jet determination, including an explicit description of their symmetry algebras.