In this article, we prove that a -homology plane with two algebraically independent -actions is isomorphic to either the affine plane or a quotient of an affine hypersurface in the affine -space via a free -action, where is the order of a finite group .
Dans cet article, on démontre qu’un plan -acyclique avec deux actions du groupe additif qui sont algébriquement indépendantes, est isomorphe au plan affine ou bien au quotient d’une hypersurface affine dans l’espace affine de dimension 3 par une action de , où est l’ordre d’un groupe fini
Keywords: ${\mathbb {Q}}$-homology plane, additive group action, Makar-Limanov invariant
Mot clés : plan ${\mathbb {Q}}$-acyclique, action du groupe additif, invariant de Makar-Limanov
@article{AIF_2003__53_2_429_0, author = {Masuda, Kayo and Miyanishi, Masayoshi}, title = {The additive group actions on ${\mathbb {Q}}$-homology planes}, journal = {Annales de l'Institut Fourier}, pages = {429--464}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {53}, number = {2}, year = {2003}, doi = {10.5802/aif.1949}, mrnumber = {1990003}, zbl = {1085.14054}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1949/} }
TY - JOUR AU - Masuda, Kayo AU - Miyanishi, Masayoshi TI - The additive group actions on ${\mathbb {Q}}$-homology planes JO - Annales de l'Institut Fourier PY - 2003 SP - 429 EP - 464 VL - 53 IS - 2 PB - Association des Annales de l’institut Fourier UR - http://www.numdam.org/articles/10.5802/aif.1949/ DO - 10.5802/aif.1949 LA - en ID - AIF_2003__53_2_429_0 ER -
%0 Journal Article %A Masuda, Kayo %A Miyanishi, Masayoshi %T The additive group actions on ${\mathbb {Q}}$-homology planes %J Annales de l'Institut Fourier %D 2003 %P 429-464 %V 53 %N 2 %I Association des Annales de l’institut Fourier %U http://www.numdam.org/articles/10.5802/aif.1949/ %R 10.5802/aif.1949 %G en %F AIF_2003__53_2_429_0
Masuda, Kayo; Miyanishi, Masayoshi. The additive group actions on ${\mathbb {Q}}$-homology planes. Annales de l'Institut Fourier, Volume 53 (2003) no. 2, pp. 429-464. doi : 10.5802/aif.1949. http://www.numdam.org/articles/10.5802/aif.1949/
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