A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00129374" target="_blank" >RIV/00216224:14310/22:00129374 - isvavai.cz</a>
Result on the web
<a href="https://arxiv.org/pdf/1905.05629.pdf" target="_blank" >https://arxiv.org/pdf/1905.05629.pdf</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.aim.2022.108590" target="_blank" >10.1016/j.aim.2022.108590</a>

Result language
angličtina
Original language name
A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3
Original language description
2-nondegenerate real hypersurfaces in complex manifolds play an important role in CR-geometry and the theory of Hermitian Symmetric Domains. In this paper, we obtain a complete convergent normal form for everywhere 2-nondegenerate real-analytic hypersurfaces in complex 3-space. We do so by entirely reproducing the Chern-Moser theory in the 2-nondegenerate setting. This seems to be the first such construction for hypersurfaces of infinite Catlin multitype. We in particular discover chains in an everywhere 2-nondegenerate hypersurface, the tangent lines to which at a point form the so-called canonical cone. Our approach is based on using a rational (nonpolynomial) model for everywhere 2-nondegenerate hypersurfaces, which is the local realization due to Fels-Kaup of the well known tube over the light cone. For the convergence of the normal form, we use an argument due to Zaitsev, based on building a canonical direction field in an appropriate bundle over a hypersurface. As an application, we obtain, in the spirit of Chern-Moser theory, a criterion for the local sphericity (i.e. local equivalence to the model) for a 2-nondegenerate hypersurface in terms of its normal form. As another application, we obtain an explicit description of the moduli space of everywhere 2-nondegenerate hypersurfaces.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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