Abstract
LetG be a complex connected reductive group. Well known wonderfulG-varieties are those of rank zero, namely the generalized flag varietiesG/P, those of rank one, classified in [A], and certain complete symmetric varieties described in [DP] such as the famous space of complete conics. Recently, there is a renewed interest in wonderful varieties of rank two since they were shown to hold a keystone position in the theory of spherical varieties, see [L], [BP], and [K].
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