# Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

Xiaojun Huang^{[1]}; Shanyu Ji^{[2]}

- [1] Rutgers University, Department of Mathematics, New Brunswick NJ 08903 (USA)
- [2] Houston University, Department of Mathematics, Houston TX 77204 (USA)

Annales de l’institut Fourier (2002)

- Volume: 52, Issue: 6, page 1793-1831
- ISSN: 0373-0956

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topHuang, Xiaojun, and Ji, Shanyu. "Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains." Annales de l’institut Fourier 52.6 (2002): 1793-1831. <http://eudml.org/doc/116028>.

@article{Huang2002,

abstract = {For a strongly pseudoconvex domain $D\subset \{\mathbb \{C\}\}^\{n+1\}$ defined by a real polynomial
of degree $k_0$, we prove that the Lie group $\{\rm Aut\}(D)$ can be identified with a
constructible Nash algebraic smooth variety in the CR structure bundle $Y$ of $\partial D$, and that the sum of its Betti numbers is bounded by a certain constant $C_\{n,k_0\}$ depending only on $n$ and $k_0$. In case $D$ is simply connected, we further give an
explicit but quite rough bound in terms of the dimension and the degree of the defining
polynomial. Our approach is to adapt the Cartan-Chern-Moser theory to the algebraic
hypersurfaces.},

affiliation = {Rutgers University, Department of Mathematics, New Brunswick NJ 08903 (USA); Houston University, Department of Mathematics, Houston TX 77204 (USA)},

author = {Huang, Xiaojun, Ji, Shanyu},

journal = {Annales de l’institut Fourier},

keywords = {real algebraic hypersurfaces; automorphism group; algebraic domains; Cartan-Chern-Moser theory; strongly pseudoconvex domain; Betti numbers},

language = {eng},

number = {6},

pages = {1793-1831},

publisher = {Association des Annales de l'Institut Fourier},

title = {Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains},

url = {http://eudml.org/doc/116028},

volume = {52},

year = {2002},

}

TY - JOUR

AU - Huang, Xiaojun

AU - Ji, Shanyu

TI - Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains

JO - Annales de l’institut Fourier

PY - 2002

PB - Association des Annales de l'Institut Fourier

VL - 52

IS - 6

SP - 1793

EP - 1831

AB - For a strongly pseudoconvex domain $D\subset {\mathbb {C}}^{n+1}$ defined by a real polynomial
of degree $k_0$, we prove that the Lie group ${\rm Aut}(D)$ can be identified with a
constructible Nash algebraic smooth variety in the CR structure bundle $Y$ of $\partial D$, and that the sum of its Betti numbers is bounded by a certain constant $C_{n,k_0}$ depending only on $n$ and $k_0$. In case $D$ is simply connected, we further give an
explicit but quite rough bound in terms of the dimension and the degree of the defining
polynomial. Our approach is to adapt the Cartan-Chern-Moser theory to the algebraic
hypersurfaces.

LA - eng

KW - real algebraic hypersurfaces; automorphism group; algebraic domains; Cartan-Chern-Moser theory; strongly pseudoconvex domain; Betti numbers

UR - http://eudml.org/doc/116028

ER -

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