Borel fixed-point theorem
From Wikipedia, the free encyclopedia
In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry. The result was proved by the Swiss mathematician Armand Borel in 1956.
[edit] Statement of the theorem
Let G be a connected, solvable algebraic group acting regularly on a non-empty, complete algebraic variety V over an algebraically closed field k. Then G has a fixed point in V.
[edit] References
- Borel, Armand (1956). "Groupes linéaires algébriques". Ann. of Math. (2) - 64: 20–82. doi:. ISSN 0003-486X. MR0093006
[edit] External links
- V.P. Platonov (2001), “Borel fixed-point theorem”, in Hazewinkel, Michiel, Encyclopaedia of Mathematics, Kluwer Academic Publishers, ISBN 978-1556080104
