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

Kód výsledku v IS VaVaI

RIV/00216224:14310/22:00129374 - isvavai.cz

Výsledek na webu

https://arxiv.org/pdf/1905.05629.pdf

DOI - Digital Object Identifier

10.1016/j.aim.2022.108590

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

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)

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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