# On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions

Annales de l'institut Fourier (1994)

- Volume: 44, Issue: 2, page 433-463
- ISSN: 0373-0956

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topHuang, Xiaojun. "On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions." Annales de l'institut Fourier 44.2 (1994): 433-463. <http://eudml.org/doc/75069>.

@article{Huang1994,

abstract = {In this paper, we show that if $M_1$ and $M_2$ are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if $f$ is a holomorphic mapping defined near a neighborhood of $M_1$ so that $f(M_1)\subset M_2$, then $f$ is also algebraic. Our proof is based on a careful analysis on the invariant varieties and reduces to the consideration of many cases. After a slight modification, the argument is also used to prove a reflection principle, which allows our main result to be stated for mappings that are holomorphic on one side and $C^\{k+1\}$ smooth up to $M_1$ where $k$ is the codimension.},

author = {Huang, Xiaojun},

journal = {Annales de l'institut Fourier},

keywords = {algebraic real hypersurfaces; holomorphic mapping; reflection principle},

language = {eng},

number = {2},

pages = {433-463},

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

title = {On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions},

url = {http://eudml.org/doc/75069},

volume = {44},

year = {1994},

}

TY - JOUR

AU - Huang, Xiaojun

TI - On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions

JO - Annales de l'institut Fourier

PY - 1994

PB - Association des Annales de l'Institut Fourier

VL - 44

IS - 2

SP - 433

EP - 463

AB - In this paper, we show that if $M_1$ and $M_2$ are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if $f$ is a holomorphic mapping defined near a neighborhood of $M_1$ so that $f(M_1)\subset M_2$, then $f$ is also algebraic. Our proof is based on a careful analysis on the invariant varieties and reduces to the consideration of many cases. After a slight modification, the argument is also used to prove a reflection principle, which allows our main result to be stated for mappings that are holomorphic on one side and $C^{k+1}$ smooth up to $M_1$ where $k$ is the codimension.

LA - eng

KW - algebraic real hypersurfaces; holomorphic mapping; reflection principle

UR - http://eudml.org/doc/75069

ER -

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## Citations in EuDML Documents

top- Joël Merker, Note on double reflection and algebraicity of holomorphic mappings
- M. S. Baouendi, L. P. Rothschild, Holomorphic mappings between algebraic hypersurfaces in complex space
- Joël Merker, On the partial algebraicity of holomorphic mappings between two real algebraic sets
- Xiaojun Huang, Shanyu Ji, Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains
- Francine Meylan, Nordine Mir, Dimitri Zaitsev, On some rigidity properties of mappings between CR-submanifolds in complex space
- Rasul Shafikov, Kausha Verma, Extension of holomorphic maps between real hypersurfaces of different dimension
- Nordine Mir, Germs of holomorphic mappings between real algebraic hypersurfaces

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