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Article

Infinite transitivity, finite generation, and Demazure roots

Advances in Mathematics. 2019. Vol. 351. P. 1-32.
Arzhantsev I., Kuyumzhiyan K., Zaidenberg M.

An affine algebraic variety X of dimension ≥2 is called flexible if the subgroup SAut(X)⊂Aut(X) generated by the one-parameter unipotent subgroups acts m-transitively on reg(X) for any m≥1. In the previous paper we proved that any nondegenerate toric affine variety X is flexible. In the present paper we show that one can find a subgroup of SAut(X) generated by a finite number of one-parameter unipotent subgroups which has the same transitivity property, provided the toric variety X is smooth in codimension two. For X=A^n with n≥2, three such subgroups suffice.