Infinite transitivity, finite generation, and Demazure roots

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.Comment: 25 page

多項式環のある指数自己同型の余順性

kを標数0の体とする．k代数k[x]の自己同型ϕが余順であるとは，ϕとアフィン自己同型全体で生成されるk[x]の自己同型群の部分群が順部分群を含むときにいう。本論分では，ある指数自己同型の余順性を決定した。首都大学東京, 2018-09-30, 修士（理学）首都大学東