In this paper, we show that if and are algebraic real hypersurfaces in (possibly different) complex spaces of dimension at least two and if is a holomorphic mapping defined near a neighborhood of so that , then 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 smooth up to where is the codimension.
Dans cet article nous montrons que si et sont des hypersurfaces algébriques réelles dans deux espaces complexes de dimension et si est une fonction holomorphe, définie dans un voisinage de , de manière à ce que , alors est aussi algébrique. Notre preuve est basée sur une analyse précise des variétés invariantes et se réduit à la considération de nombreux cas. Après une légère modification, notre argument est aussi utilisé pour prouver un principe de réflexion, qui permet une extension de notre théorème principal aux fonctions holomorphes d’un côté de et de classe , où est la codimension.
@article{AIF_1994__44_2_433_0, author = {Huang, Xiaojun}, title = {On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions}, journal = {Annales de l'Institut Fourier}, pages = {433--463}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {44}, number = {2}, year = {1994}, doi = {10.5802/aif.1405}, mrnumber = {95i:32030}, zbl = {0803.32011}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1405/} }
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 SP - 433 EP - 463 VL - 44 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1405/ DO - 10.5802/aif.1405 LA - en ID - AIF_1994__44_2_433_0 ER -
%0 Journal Article %A Huang, Xiaojun %T On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions %J Annales de l'Institut Fourier %D 1994 %P 433-463 %V 44 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1405/ %R 10.5802/aif.1405 %G en %F AIF_1994__44_2_433_0
Huang, Xiaojun. On the mapping problem for algebraic real hypersurfaces in the complex spaces of different dimensions. Annales de l'Institut Fourier, Volume 44 (1994) no. 2, pp. 433-463. doi : 10.5802/aif.1405. http://www.numdam.org/articles/10.5802/aif.1405/
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