Toute variété magnifique est sphérique |
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Authors: | D Luna |
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Institution: | (1) Institut Fourier, Université de Grenoble I, B.P. 74, F-38 402 Saint Martin d’Hères, France |
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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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Keywords: | |
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