Infinite transitivity, finite generation, and Demazure roots

Abstract

An affine algebraic variety X of dimension at least 2 is called flexible if the subgroup SAut(X) in Aut(X) generated by the one-parameter unipotent subgroups acts m-transitively on reg(X) for any m $\ge$ 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 2. For X=${\mathbb{A}}^n$ with n$\ge$2, three such subgroups suffice.

25 pages

References in corpus (4)

• On the geometry of the automorphism groups of affine varieties
• On the tame authomorphism approximation, augmentation Topology of Automorphism Groups and $Ind$-schemes, and authomorphisms of tame automorphism groups
• On nilpotent generators of the special linear Lie algebra
• Integrable generators of Lie algebras of vector fields on ${\mathbb{C}}^n$

Cited by in corpus (5)

• Tits type alternative for groups acting on toric affine varieties
• Automorphisms of algebraic varieties and infinite transitivity
• On the automorphism group of non-necessarily normal affine toric varieties
• Root subgroups on affine spherical varieties
• Tits-type alternative for certain groups acting on algebraic surfaces