Equivariant Embeddings of Commutative Linear Algebraic Groups of Corank One
- Ivan Arzhantsev, Polina Kotenkova, Thomas Peternell
We say that a group G acts infinitely transitively on a set X if for every m ∈ N the induced diagonal action of G is transitive on the cartesian mth power Xm \∆ with the diagonals removed. We describe three classes of affine algebraic varieties such that their automorphism groups act infinitely transitively on their smooth loci. The first class consists of affine cones over flag varieties, the second of non-degenerate affine toric varieties, and the third of iterated suspensions over affine varieties with infinitely transitive automorphism groups of a reinforced type.