Fixed points for reductive group actions on acyclic varieties

Martin Fankhauser

Annales de l'institut Fourier (1995)

  • Volume: 45, Issue: 5, page 1249-1281
  • ISSN: 0373-0956

Abstract

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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 .

How to cite

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Fankhauser, Martin. "Fixed points for reductive group actions on acyclic varieties." Annales de l'institut Fourier 45.5 (1995): 1249-1281. <http://eudml.org/doc/75159>.

@article{Fankhauser1995,
abstract = {Let $X$ be a smooth, affine complex variety, which, considered as a complex manifold, has the singular $\{\Bbb Z\}$-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 $\pi :X\rightarrow X/\!\!/G$ contains a dense orbit. If $G$ is connected and reductive, then the action has fixed points if $\{\rm dim\}\,X/\!\!/G\le 3$.},
author = {Fankhauser, Martin},
journal = {Annales de l'institut Fourier},
keywords = {action of complex algebraic group; quotient; fixed points},
language = {eng},
number = {5},
pages = {1249-1281},
publisher = {Association des Annales de l'Institut Fourier},
title = {Fixed points for reductive group actions on acyclic varieties},
url = {http://eudml.org/doc/75159},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Fankhauser, Martin
TI - Fixed points for reductive group actions on acyclic varieties
JO - Annales de l'institut Fourier
PY - 1995
PB - Association des Annales de l'Institut Fourier
VL - 45
IS - 5
SP - 1249
EP - 1281
AB - Let $X$ be a smooth, affine complex variety, which, considered as a complex manifold, has the singular ${\Bbb Z}$-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 $\pi :X\rightarrow X/\!\!/G$ contains a dense orbit. If $G$ is connected and reductive, then the action has fixed points if ${\rm dim}\,X/\!\!/G\le 3$.
LA - eng
KW - action of complex algebraic group; quotient; fixed points
UR - http://eudml.org/doc/75159
ER -

References

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