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Borel fixed-point theorem

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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): 20–82. ISSN 0003-486X. {{cite journal}}: Text "volume - 64" ignored (help) MR0093006
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