no. 2
The additive group actions on ℚ-homology planes
[Actions du groupe additif sur des plans ℚ-acycliques]
Masuda, Kayo1 ; Miyanishi, Masayoshi
1 Himeji Institute of Technology, Mathematical Sciences II, 2167 Shosha, Himeji 671-2201 (Japon)
Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 429-464.

Dans cet article, on démontre qu’un plan ℚ-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 ℤ/mℤ, où m est l’ordre d’un groupe fini H 1 (X;ℤ)

In this article, we prove that a ℚ-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 ℤ/mℤ-action, where m is the order of a finite group H 1 (X;ℤ).

DOI : 10.5802/aif.1949
Classification : 14L30, 14R20, 14J26
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 

1 Himeji Institute of Technology, Mathematical Sciences II, 2167 Shosha, Himeji 671-2201 (Japon) 
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Masuda, Kayo; Miyanishi, Masayoshi. The additive group actions on ${\mathbb {Q}}$-homology planes. Annales de l'Institut Fourier, Tome 53 (2003) no. 2, pp. 429-464. doi : 10.5802/aif.1949. https://aif.centre-mersenne.org/articles/10.5802/aif.1949/

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