The additive group actions on -homology planes
Annales de l'Institut Fourier, Volume 53 (2003) no. 2, p. 429-464
In this article, we prove that a -homology plane X with two algebraically independent G a -actions is isomorphic to either the affine plane or a quotient of an affine hypersurface xy=z m -1 in the affine 3-space via a free /m-action, where m is the order of a finite group H 1 (X;).
Dans cet article, on démontre qu’un plan -acyclique X avec deux actions du groupe additif G a qui sont algébriquement indépendantes, est isomorphe au plan affine ou bien au quotient d’une hypersurface affine xy=z n -1 dans l’espace affine de dimension 3 par une action de /m, où m est l’ordre d’un groupe fini H 1 (X;)
DOI : https://doi.org/10.5802/aif.1949
Classification:  14L30,  14R20,  14J26
Keywords: -homology plane, additive group action, Makar-Limanov invariant
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {53},
     number = {2},
     year = {2003},
     pages = {429-464},
     doi = {10.5802/aif.1949},
     mrnumber = {1990003},
     zbl = {1085.14054},
     language = {en},
     url = {https://aif.centre-mersenne.org/item/AIF_2003__53_2_429_0}
}
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/item/AIF_2003__53_2_429_0/

[3] S. Bundagaard; J. Nielsen On normal subgroups with finite index in F-groups, Math. Tidsskrift, Tome B (1951), pp. 56-98 | MR 48447 | Zbl 0044.25403

[1] T. Bandman; L. Makar-Limanov Affine surfaces with A K ( S ) = , Michigan J. Math, Tome 49 (2001), pp. 567-582 | Article | MR 1872757 | Zbl 01742561

[2] J. Bertin Pinceaux de droites et automorphismes des surfaces affines, J. reine. angew. Math, Tome 341 (1983), pp. 32-53 | Article | MR 697306 | Zbl 0501.14028

[4] K.-H. Fieseler On complex affine surfaces with + -action, Comment. Math. Helvetici, Tome 69 (1994), pp. 5-27 | Article | MR 1259603 | Zbl 0806.14033

[5] R. H. Fox On Fenchel's conjecture about F-groups, Math. Tidsskrift, Tome B (1952), pp. 61-65 | MR 53937 | Zbl 0049.15404

[6] R.V. Gurjar; M. Miyanishi On the Jacobian conjecture for -homology planes, J. reine angew. Math, Tome 516 (1999), pp. 115-132 | Article | MR 1724617 | Zbl 0954.14042

[7] R.V. Gurjar; C.R. Pradeep -homology planes are rational. III, Osaka J. Math, Tome 36 (1999) no. 2, pp. 259-335 | MR 1736480 | Zbl 0954.14013

[8] S. Kaliman; L. Makar-Limanov On the Russell-Koras contractible threefolds. J. Algebraic Geom, J. Algebraic Geom, Tome 6 (1997) no. 2, pp. 247-268 | MR 1489115 | Zbl 0897.14010

[9] K. Masuda; M. Miyanishi Étale endomorphisms of algebraic surfaces with G m -actions, Math. Ann, Tome 319 (2001), pp. 493-516 | Article | MR 1819880 | Zbl 1016.14028

[10] M. Miyanishi Curves on rational and unirational surfaces, Springer, Lecture Notes at Tata Institute of Fundamental Research (1978) | MR 546289 | Zbl 0425.14008

[11] M. Miyanishi; K. Masuda Generalized Jacobian conjecture and related topics, Proceedings of the International Colloquium on Algebra, Arithmetic and Geometry, Mumbai 2000, Tata Institute of Fundamental Research, Narosa (2002) | Zbl 1053.14071

[12] M. Miyanishi; T. Sugie Homology planes with quotient singularities, J. Math. Kyoto Univ, Tome 31 (1991), pp. 755-788 | MR 1127098 | Zbl 0790.14034