Modification of Poincare'sconstruction and its application in $CR$-geometry of hypersurfaces in $\mathbf{C}^4$

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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. $20$).

作者简介

Valerii 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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