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

Abstract

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For a strongly pseudoconvex domain D ⊂ ℂ n + 1 defined by a real polynomial of degree k 0 , we prove that the Lie group Aut ( D ) can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle Y of ∂ 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.

How to cite

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Huang, 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 -

References

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