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Transformation Groups

, Volume 1, Issue 3, pp 249–258 | Cite as

Toute variété magnifique est sphérique

Article

Abstract

LetG be a (connected) reductive group (over C). An algebraicG-varietyX is called “wonderful”, if the following conditions are satisfied:X is (connected) smooth and complete;X containsr irreducible smoothG-invariant divisors having a non void transversal intersection;G has 2 r orbits inX. We show that wonderful varieties are necessarily spherical (i.e., they are almost homogeneous under any Borel subgroup ofG).

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Copyright information

© Birkhäuser 1996

Authors and Affiliations

  • D. Luna
    • 1
  1. 1.Institut FourierUniversité de Grenoble ISaint Martin d’HèresFrance

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