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
Masuda, Kayo 1; Miyanishi, Masayoshi 
@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}, zbl = {1085.14054}, mrnumber = {1990003}, language = {en}, url = {https://aif.centre-mersenne.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 - https://aif.centre-mersenne.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 https://aif.centre-mersenne.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. https://aif.centre-mersenne.org/articles/10.5802/aif.1949/
[3] On normal subgroups with finite index in F-groups, Math. Tidsskrift, Volume B (1951), pp. 56-98 | MR | Zbl
[1] Affine surfaces with , Michigan J. Math, Volume 49 (2001), pp. 567-582 | DOI | MR | Zbl
[2] Pinceaux de droites et automorphismes des surfaces affines, J. reine. angew. Math, Volume 341 (1983), pp. 32-53 | DOI | MR | Zbl
[4] On complex affine surfaces with -action, Comment. Math. Helvetici, Volume 69 (1994), pp. 5-27 | DOI | MR | Zbl
[5] On Fenchel's conjecture about F-groups, Math. Tidsskrift, Volume B (1952), pp. 61-65 | MR | Zbl
[6] On the Jacobian conjecture for -homology planes, J. reine angew. Math, Volume 516 (1999), pp. 115-132 | DOI | MR | Zbl
[7] -homology planes are rational. III, Osaka J. Math, Volume 36 (1999) no. 2, pp. 259-335 | MR | Zbl
[8] On the Russell-Koras contractible threefolds. J. Algebraic Geom, J. Algebraic Geom, Volume 6 (1997) no. 2, pp. 247-268 | MR | Zbl
[9] Étale endomorphisms of algebraic surfaces with -actions, Math. Ann, Volume 319 (2001), pp. 493-516 | DOI | MR | Zbl
[10] Curves on rational and unirational surfaces, Lecture Notes at Tata Institute of Fundamental Research, Springer, 1978 | MR | Zbl
[11] Generalized Jacobian conjecture and related topics, Proceedings of the International Colloquium on Algebra, Arithmetic and Geometry, Mumbai 2000, Tata Institute of Fundamental Research (2002) | Zbl
[12] Homology planes with quotient singularities, J. Math. Kyoto Univ, Volume 31 (1991), pp. 755-788 | MR | Zbl
Cited by Sources: