Uniqueness questions in real algebraic transformation groups
Let \(G\) be a compact Lie group and \(H\) a closed subgroup. The authors show that the homogeneous space \(G/H\) has a unique structure as a real algebraic \(G\)-variety. For a real algebraic \(G\)-variety they show that the balanced product \(G\times_H X\) has the structure of a real algebraic \(G\)-variety, and this structure is uniquely determined by the structure on \(X\). On the other hand, suppose that \(M\) is a closed smooth \(G\)-manifold with positive dimensional orbit space \(M/G\). If \(M\) has a \(G\)-equivariant real algebraic model, then it has an uncountable family of birationally inequivariant such models.
scientific article; zbMATH DE number 1746064
scientific article