A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3
Identifikátory výsledku
Kód výsledku v 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>
Výsledek na webu
<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>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3
Popis výsledku v původním jazyce
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.
Název v anglickém jazyce
A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3
Popis výsledku anglicky
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.
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Advances in Mathematics
ISSN
0001-8708
e-ISSN
1090-2082
Svazek periodika
408
Číslo periodika v rámci svazku
October
Stát vydavatele periodika
US - Spojené státy americké
Počet stran výsledku
37
Strana od-do
1-37
Kód UT WoS článku
000860924200011
EID výsledku v databázi Scopus
2-s2.0-85134933539