The additive group actions on ${\mathbb {Q}}$-homology planes

Masuda, Kayo; Miyanishi, Masayoshi

The additive group actions on

ℚ

-homology planes
[Actions du groupe additif sur des plans

ℚ

-acycliques]

Masuda, Kayo ; Miyanishi, Masayoshi

Annales de l'Institut Fourier, Tome 53 (2003), p. 429-464 / Harvested from Numdam

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Résumé
Abstract

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 $x y = z^{n} - 1$ dans l’espace affine de dimension 3 par une action de $ℤ / m ℤ$ , 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 $x y = z^{m} - 1$ in the affine $3$ -space via a free $ℤ / m ℤ$ -action, where $m$ is the order of a finite group $H_{1} (X; ℤ)$ .

Publié le : 2003-01-01

MR 1990003 | Zbl 1085.14054

DOI : https://doi.org/10.5802/aif.1949
Classification: 14L30, 14R20, 14J26
Mots clés: plan

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},
     volume = {53},
     year = {2003},
     pages = {429-464},
     doi = {10.5802/aif.1949},
     mrnumber = {1990003},
     zbl = {1085.14054},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2003__53_2_429_0}
}

Masuda, Kayo; Miyanishi, Masayoshi. The additive group actions on ${\mathbb {Q}}$-homology planes. Annales de l'Institut Fourier, Tome 53 (2003) pp. 429-464. doi : 10.5802/aif.1949. http://gdmltest.u-ga.fr/item/AIF_2003__53_2_429_0/

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