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Quelques propriétés des espaces homogènes sphériques. (Some properties of spherical homogeneous spaces). (French) Zbl 0604.14048
Let G be a connected reductive algebraic group over an algebraically closed field of characteristic zero, and let H be a closed subgroup of G. The homogeneous space G/H is called ”spherical”, iff the action of a Borel subgroup of G has a dense orbit in G/H. For example, if H contains a maximal unipotent subgroup of G, or if G/H is a symmetric space, then G/H is spherical.
The author proves that any spherical homogeneous space G/H is a deformation of a homogeneous space \(G/H_ 0\), where \(H_ 0\) contains a maximal unipotent subgroup of G. This implies that the action of a Borel subgroup of G on a spherical homogeneous space G/H has only a finite number of orbits.
Reviewer: F.Pauer

MSC:
14M17 Homogeneous spaces and generalizations
20G15 Linear algebraic groups over arbitrary fields
14L30 Group actions on varieties or schemes (quotients)
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