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 (G:X×X * ), 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 (G:X) 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 (G:X×X * )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 (G:X). 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},
     zbl = {0831.14022},
     mrnumber = {96i:14039},
     language = {en},
     url = {http://www.numdam.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. http://www.numdam.org/item/AIF_1995__45_4_929_0/

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