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<p>An intriguing phenomenon regarding Levi-degenerate hypersurfaces is the existence of nontrivial infinitesimal symmetries with vanishing 2-jets at a&#xa0;point. In this work we consider polynomial models of Levi-degenerate real hypersurfaces in <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbb {C}^3\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mn>3</mn> </msup> </math></EquationSource> </InlineEquation> 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.</p>

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Classification of Polynomial Models Without 2-Jet Determination in \(\mathbb {C}^3\)

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月30日

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  • Martin Kolář,
  • Petr Liczman,
  • Francine Meylan

摘要

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 \(\mathbb {C}^3\) 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.