Let be a smooth, affine complex variety, which, considered as a complex manifold, has the singular -cohomology of a point. Suppose that is a complex algebraic group acting algebraically on . Our main results are the following: if is semi-simple, then the generic fiber of the quotient map contains a dense orbit. If is connected and reductive, then the action has fixed points if .
Soit une variété complexe, affine et lisse, qui, considérée comme variété analytique, a la -cohomologie singulière d’un point. Supposons que soit un groupe complexe algébrique agissant algébriquement sur . Nos résultats principaux sont les suivants : Si est semisimple, la fibre générique de l’application quotient contient une orbite dense. Si est connexe et réductif, l’action a des points fixes si .
@article{AIF_1995__45_5_1249_0, author = {Fankhauser, Martin}, title = {Fixed points for reductive group actions on acyclic varieties}, journal = {Annales de l'Institut Fourier}, pages = {1249--1281}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {5}, year = {1995}, doi = {10.5802/aif.1495}, mrnumber = {97a:14047}, zbl = {0834.14027}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1495/} }
TY - JOUR AU - Fankhauser, Martin TI - Fixed points for reductive group actions on acyclic varieties JO - Annales de l'Institut Fourier PY - 1995 SP - 1249 EP - 1281 VL - 45 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1495/ DO - 10.5802/aif.1495 LA - en ID - AIF_1995__45_5_1249_0 ER -
%0 Journal Article %A Fankhauser, Martin %T Fixed points for reductive group actions on acyclic varieties %J Annales de l'Institut Fourier %D 1995 %P 1249-1281 %V 45 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1495/ %R 10.5802/aif.1495 %G en %F AIF_1995__45_5_1249_0
Fankhauser, Martin. Fixed points for reductive group actions on acyclic varieties. Annales de l'Institut Fourier, Volume 45 (1995) no. 5, pp. 1249-1281. doi : 10.5802/aif.1495. http://archive.numdam.org/articles/10.5802/aif.1495/
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