no. 5
Fixed points for reductive group actions on acyclic varieties
Annales de l'Institut Fourier, Tome 45 (1995) no. 5, pp. 1249-1281.

Soit X une variété complexe, affine et lisse, qui, considérée comme variété analytique, a la ℤ-cohomologie singulière d’un point. Supposons que G soit un groupe complexe algébrique agissant algébriquement sur X. Nos résultats principaux sont les suivants : Si G est semisimple, la fibre générique de l’application quotient π:X→X//G contient une orbite dense. Si G est connexe et réductif, l’action a des points fixes si dim X//G≤3.

Let X be a smooth, affine complex variety, which, considered as a complex manifold, has the singular ℤ-cohomology of a point. Suppose that G is a complex algebraic group acting algebraically on X. Our main results are the following: if G is semi-simple, then the generic fiber of the quotient map π:X→X//G contains a dense orbit. If G is connected and reductive, then the action has fixed points if dim X//G≤3.

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     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},
     zbl = {0834.14027},
     mrnumber = {97a:14047},
     language = {en},
     url = {https://aif.centre-mersenne.org/articles/10.5802/aif.1495/}
}
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Fankhauser, Martin. Fixed points for reductive group actions on acyclic varieties. Annales de l'Institut Fourier, Tome 45 (1995) no. 5, pp. 1249-1281. doi : 10.5802/aif.1495. https://aif.centre-mersenne.org/articles/10.5802/aif.1495/

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