Models of 2-nondegenerate CR hypersurfaces in C^N

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F25%3A00144417" target="_blank" >RIV/00216224:14310/25:00144417 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61988987:17310/25:A2603AWL

Výsledek na webu

<a href="https://link.springer.com/article/10.1007/s00208-025-03138-1" target="_blank" >https://link.springer.com/article/10.1007/s00208-025-03138-1</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00208-025-03138-1" target="_blank" >10.1007/s00208-025-03138-1</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Models of 2-nondegenerate CR hypersurfaces in C^N

Popis výsledku v původním jazyce

We show that every point in a uniformly 2-nondegenerate CR hypersurface is canonically associated with a model 2-nondegenerate structure. The 2-nondegenerate models which we introduce are essential CR invariants playing the same fundamental role as quadrics do in the classical Levi nondegenerate case. In particular, we show that each real analytic uniformly 2-nondegenerate hypersurface in {mathbb {C}}^N is a perturbation of a 2-nondegenerate model. We give a complete characterization of all 2-nondegenerate models and show that the moduli space of such hypersurfaces in {mathbb {C}}^N is infinite dimensional for each N&gt;3. We derive a normal form for these models' defining equations that is unique up to an action of a finite dimensional Lie group. We generalize recently introduced CR invariants (modified symbols), and show how to compute these intrinsically defined invariants from a model's defining equation. Moreover, we show that these models automatically possess infinitesimal symmetries spanning a complement to their Levi kernel and derive explicit formulas for such symmetries.

Název v anglickém jazyce

Models of 2-nondegenerate CR hypersurfaces in C^N

Popis výsledku anglicky

We show that every point in a uniformly 2-nondegenerate CR hypersurface is canonically associated with a model 2-nondegenerate structure. The 2-nondegenerate models which we introduce are essential CR invariants playing the same fundamental role as quadrics do in the classical Levi nondegenerate case. In particular, we show that each real analytic uniformly 2-nondegenerate hypersurface in {mathbb {C}}^N is a perturbation of a 2-nondegenerate model. We give a complete characterization of all 2-nondegenerate models and show that the moduli space of such hypersurfaces in {mathbb {C}}^N is infinite dimensional for each N&gt;3. We derive a normal form for these models' defining equations that is unique up to an action of a finite dimensional Lie group. We generalize recently introduced CR invariants (modified symbols), and show how to compute these intrinsically defined invariants from a model's defining equation. Moreover, we show that these models automatically possess infinitesimal symmetries spanning a complement to their Levi kernel and derive explicit formulas for such symmetries.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GC22-15012J" target="_blank" >GC22-15012J: Hladká a analytická regularita v CR geometrii</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

Kód důvěrnosti údajů

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

Název periodika

Mathematische Annalen

ISSN

0025-5831

e-ISSN

1432-1807

Svazek periodika

392

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

49

Strana od-do

1615-1663

Kód UT WoS článku

001468403400001

EID výsledku v databázi Scopus

2-s2.0-105000483469