ANNALES DE L'INSTITUT FOURIER

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

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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. https://aif.centre-mersenne.org/articles/10.5802/aif.1479/

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