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

J 2022

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

KOLÁŘ, Martin a Ilja KOSSOVSKIY

Základní údaje

Originální název

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

Autoři

KOLÁŘ, Martin a Ilja KOSSOVSKIY

Vydání

Advances in Mathematics, Academic Press Inc. 2022, 0001-8708

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL, URL

Impakt faktor

Impact factor: 1.700

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/22:00129374

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

CR-manifolds; Normal forms; Automorphism group; Holomorphic mappings

Štítky

14311010, H24, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 17. 1. 2023 14:42, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA17-19437S, projekt VaV

Název: Klasifikační problémy pro reálné nadplochy v komplexním prostoru

Investor: Grantová agentura ČR, Klasifikační problémy pro reálné nadplochy v komplexním prostoru

GA21-09220S, projekt VaV

Název: Invarianty a symetrie Levi degenerovaných CR variet (Akronym: InSyLeD)

Investor: Grantová agentura ČR, Invarianty a symetrie Levi degenerovaných CR variet

Citovat

KOLÁŘ, Martin a Ilja KOSSOVSKIY. A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3. Advances in Mathematics. Academic Press Inc., 2022, roč. 408, October, s. 1-37. ISSN 0001-8708. Dostupné z: https://doi.org/10.1016/j.aim.2022.108590.

@article{2247383,
   author = {Kolář, Martin and Kossovskiy, Ilja},
   article_number = {October},
   doi = {https://doi.org/10.1016/j.aim.2022.108590},
   keywords = {CR-manifolds; Normal forms; Automorphism group; Holomorphic mappings},
   language = {eng},
   issn = {0001-8708},
   journal = {Advances in Mathematics},
   title = {A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3},
   url = {https://arxiv.org/pdf/1905.05629.pdf},
   volume = {408},
   year = {2022}
}

TY  - JOUR
ID  - 2247383
AU  - Kolář, Martin - Kossovskiy, Ilja
PY  - 2022
TI  - A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3
JF  - Advances in Mathematics
VL  - 408
IS  - October
SP  - 1-37
EP  - 1-37
PB  - Academic Press Inc.
SN  - 00018708
KW  - CR-manifolds
KW  - Normal forms
KW  - Automorphism group
KW  - Holomorphic mappings
UR  - https://arxiv.org/pdf/1905.05629.pdf
N2  - 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.
ER  -

KOLÁŘ, Martin a Ilja KOSSOVSKIY. A complete normal form for everywhere Levi-degenerate hypersurfaces in C-3. \textit{Advances in Mathematics}. Academic Press Inc., 2022, roč.~408, October, s.~1-37. ISSN~0001-8708. Dostupné z: https://doi.org/10.1016/j.aim.2022.108590.

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