Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
Result description
We construct a complete convergent normal form for a real hypersurface in C^N for N>1 at a generic Levi-degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. As an application of the convergence result, we obtain an explicit description of the moduli space of germs of real-analytic hypersurfaces with a generic Levi-degeneracy. As another application, we obtain, in the spirit of the work of Chern and Moser, distinguished curves inside the Levi-degeneracy set that we call degenerate chains.
Keywords
The result's identifiers
Result code in IS VaVaI
Result on the web
https://www.degruyter.com/view/j/crelle.2019.2019.issue-749/crelle-2016-0034/crelle-2016-0034.xml
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
Original language description
We construct a complete convergent normal form for a real hypersurface in C^N for N>1 at a generic Levi-degeneracy. This seems to be the first convergent normal form for a Levi-degenerate hypersurface. As an application of the convergence result, we obtain an explicit description of the moduli space of germs of real-analytic hypersurfaces with a generic Levi-degeneracy. As another application, we obtain, in the spirit of the work of Chern and Moser, distinguished curves inside the Levi-degeneracy set that we call degenerate chains.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
GA17-19437S: Classification problems for real hypersurfaces in complex space
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal für die Reine und Angewandte Mathematik
ISSN
0075-4102
e-ISSN
1435-5345
Volume of the periodical
749
Issue of the periodical within the volume
1
Country of publishing house
DE - GERMANY
Number of pages
25
Pages from-to
201-225
UT code for WoS article
000462744900006
EID of the result in the Scopus database
2-s2.0-85064228323
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Pure mathematics
Year of implementation
2019