Given an irreducible affine algebraic variety of dimension , we let denote the special automorphism group of , that is, the subgroup of the full automorphism group generated by all one-parameter unipotent subgroups. We show that if is transitive on the smooth locus , then it is infinitely transitive on . In turn, the transitivity is equivalent to the flexibility of . The latter means that for every smooth point the tangent space is spanned by the velocity vectors at of one-parameter unipotent subgroups of . We also provide various modifications and applications.
"Flexible varieties and automorphism groups." Duke Math. J. 162 (4) 767 - 823, 15 March 2013. https://doi.org/10.1215/00127094-2080132