论文标题
自由群体的自动形态群体的嵌入到仿期代数品种的自动形态群体中
Embeddings of automorphism groups of free groups into automorphism groups of affine algebraic varieties
论文作者
论文摘要
构建了一个新的无限仿射代数品种，其自动形态组包含自由组$ {\ rm aut}（f_n）$的自动形态组$ f_n）$ f_n $ f_n $等级$ n $。此类品种的自动形态组是非线性的，并且包含$ n $ n $ strands in $ n \ geqslant 3 $的编织组$ b_n $，并且对于$ n \ geqslant 2 $而言不合同。作为一个应用程序，证明对于$ n \ geqslant 3 $，每个等级的cremona组$ \ geqslant 3n-1 $包含$ {\ rm aut}（f_n）$和$ b_n $的组。这一界限比作者之前发表的界限要好1个。关于$ b_n $，其增长率的订单比D. Krammer的论文限制的订单低一个。构造的基础是三胞胎$（g，r，n）$，其中$ g $是连接的半胶合代数组，$ r $是其最大圆环的封闭子组。
A new infinite series of rational affine algebraic varieties is constructed whose automorphism group contains the automorphism group ${\rm Aut}(F_n)$ of the free group $F_n$ of rank $n$. The automorphism groups of such varieties are nonlinear and contain the braid group $B_n$ on $n$ strands for $n\geqslant 3$, and are nonamenable for $n\geqslant 2$. As an application, it is proved that for $n\geqslant 3$, every Cremona group of rank $\geqslant 3n-1$ contains the groups ${\rm Aut}(F_n)$ and $B_n$. This bound is 1 better than the one published earlier by the author; with respect to $B_n$ the order of its growth rate is one less than that of the bound following from the paper by D. Krammer. The basis of the construction are triplets $(G, R, n)$, where $G$ is a connected semisimple algebraic group and $R$ is a closed subgroup of its maximal torus.
