A modification of Poincare's construction and its application to the CR geometry of hypersurfaces in ${\bf C}^4$

V. K. Beloshapka

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arXiv · 2102.06451

A modification of Poincare's construction and its application to the CR geometry of hypersurfaces in ${\bf C}^4$

V. K. Beloshapka

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Abstract

A generalization of the homological Poincare's operator was used to estimate the dimension of the Lie algebra of infinitesimal holomorphic automorphisms of an arbitrary germ of a real analytic hypersurface in ${\bf C}^4$. The following alternative is proved: either this dimension is infinite, or it does not exceed 24. Value 24 takes place only for one of two nondegenerate hyperquadrics. If the hypersurface is 2-nondegenerate at a generic point, then the dimension does not exceed 17, and if the hypersurface is 3-nondegenerate at a generic point, then the estimate is 20.

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BibTeX RIS

V. K. Beloshapka. 2021-02-12. A modification of Poincare's construction and its application to the CR geometry of hypersurfaces in ${\bf C}^4$. https://arxiv.org/abs/2102.06451

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