# ANNALES DE L'INSTITUT FOURIER

Reductive group actions on affine varieties and their doubling
Annales de l'Institut Fourier, Volume 45 (1995) no. 4, p. 929-950

We study $G$-actions of the form $\left(G:X×{X}^{*}\right)$, where ${X}^{*}$ is the dual (to $X$) $G$-variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action $\left(G:X\right)$ is given. It is shown that the doubled actions have a number of nice properties, if $X$ is spherical or of complexity one.

Nous étudions les actions de la forme $\left(G:X×{X}^{*}\right)$${X}^{*}$ est la $G$-variété duale de $X$. Ces actions sont appelées les doubles. Nous donnons une interprétation géométrique de la complexité de l’action $\left(G:X\right)$. Nous montrons que les actions doublées ont un certain nombre de bonnes propriétés, lorsque $X$ est sphérique ou de complexité un.

@article{AIF_1995__45_4_929_0,
author = {Panyushev, Dmitri I.},
title = {Reductive group actions on affine varieties and their doubling},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l'institut Fourier},
volume = {45},
number = {4},
year = {1995},
pages = {929-950},
doi = {10.5802/aif.1479},
mrnumber = {96i:14039},
zbl = {0831.14022},
language = {en},
url = {https://aif.centre-mersenne.org/item/AIF_1995__45_4_929_0}
}

Panyushev, Dmitri I. Reductive group actions on affine varieties and their doubling. Annales de l'Institut Fourier, Volume 45 (1995) no. 4, pp. 929-950. doi : 10.5802/aif.1479. aif.centre-mersenne.org/item/AIF_1995__45_4_929_0/

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