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EZHOV, Vladimir, Martin KOLÁŘ a Gerd SCHMALZ. Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C-2. INDIANA UNIVERSITY MATHEMATICS JOURNAL. 2013, roč. 62, č. 1, s. 1-32. ISSN 0022-2518.

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Základní údaje
Originální název	Normal Forms and Symmetries of Real Hypersurfaces of Finite Type in C-2
Autoři	EZHOV, Vladimir (36 Austrálie), Martin KOLÁŘ (203 Česká republika, garant, domácí) a Gerd SCHMALZ (276 Německo).
Vydání	INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2013, 0022-2518.

Další údaje
Originální jazyk	angličtina
Typ výsledku	Článek v odborném periodiku
Obor	10101 Pure mathematics
Stát vydavatele	Spojené státy
Utajení	není předmětem státního či obchodního tajemství
Impakt faktor	Impact factor: 0.358
Kód RIV	RIV/00216224:14310/13:00067030
Organizační jednotka	Přírodovědecká fakulta
UT WoS	000329473200001
Klíčová slova anglicky	Normal form real hypersurface symmetry algebra
Štítky	AKR, automorphism, finite type hypersurfaces, rivok, stability group
Příznaky	Mezinárodní význam, Recenzováno
Změnil	Změnila: Ing. Andrea Mikešková, učo 137293. Změněno: 8. 4. 2014 13:45.

Anotace
We give a complete description of normal forms for real hypersurfaces of finite type in C-2 with respect to their holomorphic symmetry algebras. The normal forms include refined versions of the constructions by Chern-Moser, Stanton, Kolar. We use the method of simultaneous normalisation of the equations and symmetries that goes back to Lie and Cartan. Our approach leads to a unique canonical equation of the hypersurface for every type of its symmetry algebra. Moreover, even in the Levi-degenerate case, our construction implies convergence of the transformation to the normal form if the dimension of the symmetry algebra is at least two. We illustrate our results by explicitly normalising Cartan's homogeneous hypersurfaces and their automorphisms.

Anotace

We give a complete description of normal forms for real hypersurfaces of finite type in C-2 with respect to their holomorphic symmetry algebras. The normal forms include refined versions of the constructions by Chern-Moser, Stanton, Kolar. We use the method of simultaneous normalisation of the equations and symmetries that goes back to Lie and Cartan. Our approach leads to a unique canonical equation of the hypersurface for every type of its symmetry algebra. Moreover, even in the Levi-degenerate case, our construction implies convergence of the transformation to the normal form if the dimension of the symmetry algebra is at least two. We illustrate our results by explicitly normalising Cartan's homogeneous hypersurfaces and their automorphisms.

Návaznosti
GA201/08/0397, projekt VaV	Název: Algebraické metody v geometrii a topologii
GA201/08/0397, projekt VaV	Investor: Grantová agentura ČR, Algebraické metody v geometrii a topologii