Borel fixed-point theorem

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.

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.

References

• Borel, Armand (1956). "Groupes linéaires algébriques". Ann. of Math. (2). - 64: 20–82. doi:10.2307/1969949. ISSN 0003-486X. MR0093006

External links

• V.P. Platonov (2001) [1994], "Borel fixed-point theorem", Encyclopedia of Mathematics, EMS Press