Modification of Poincare'sconstruction and its application in $CR$-geometry of hypersurfaces in $\mathbf{C}^4$
- Authors: Beloshapka V.K.1,2
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Affiliations:
- Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
- Moscow Center for Fundamental and Applied Mathematics
- Issue: Vol 86, No 5 (2022)
- Pages: 18-42
- Section: Articles
- URL: https://journals.rcsi.science/1607-0046/article/view/133879
- DOI: https://doi.org/10.4213/im9249
- ID: 133879
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Abstract
The modified Poincare construction (a generalization of Poincare's homological operator)was earlier used to estimate the dimension of the local automorphism group for an arbitrary germof a real-analytic hypersurface in $\mathbf{C}^3$. In the present paper we prove the followingalternative. For every hypersurface in $\mathbf{C}^4$, this dimension is either infinite or doesnot exceed $24$. Moreover, $24$ occurs only for a non-degenerate hyperquadric(one of the two). If the hypersurface is $2$-nondegenerate (resp. $3$-non-degenerate)at a generic point, the bound can be improved to $17$ (resp. $20$).
Keywords
About the authors
Valerii Konstantinovich Beloshapka
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Moscow Center for Fundamental and Applied Mathematics
Email: vkb@strogino.ru
Doctor of physico-mathematical sciences, Professor
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