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Funktsional. Anal. i Prilozhen., 2000, Volume 34, Issue 1, Pages 41–50 (Mi faa281)  

On Fixed Points of Algebraic Actions on $\mathbb{C}^n$

P. I. Katsyloa, V. L. Popovb

a Independent University of Moscow
b Moscow State Institute of Electronics and Mathematics (Technical University)

Abstract: It is shown that the action regarded for a rather long time by experts as a possible example disproving the conjecture on the existence of fixed points for reductive algebraic group actions on affine spaces is not an action on an affine variety, and therefore provides no example of this kind. Moreover, it is shown that the actions naturally related to the original one provide no examples of this kind as well.

DOI: https://doi.org/10.4213/faa281

Full text: PDF file (1038 kB)
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English version:
Functional Analysis and Its Applications, 2000, 34:1, 33–40

Bibliographic databases:

UDC: 512.743
Received: 01.09.1998

Citation: P. I. Katsylo, V. L. Popov, “On Fixed Points of Algebraic Actions on $\mathbb{C}^n$”, Funktsional. Anal. i Prilozhen., 34:1 (2000), 41–50; Funct. Anal. Appl., 34:1 (2000), 33–40

Citation in format AMSBIB
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\by P.~I.~Katsylo, V.~L.~Popov
\paper On Fixed Points of Algebraic Actions on $\mathbb{C}^n$
\jour Funktsional. Anal. i Prilozhen.
\yr 2000
\vol 34
\issue 1
\pages 41--50
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\crossref{https://doi.org/10.4213/faa281}
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\zmath{https://zbmath.org/?q=an:0989.14016}
\transl
\jour Funct. Anal. Appl.
\yr 2000
\vol 34
\issue 1
\pages 33--40
\crossref{https://doi.org/10.1007/BF02467065}
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