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 2r 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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Luna, D. Toute variété magnifique est sphérique. Transformation Groups 1, 249–258 (1996). https://doi.org/10.1007/BF02549208
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DOI: https://doi.org/10.1007/BF02549208