发表机构
National Research University Higher School of Economics; Steklov Mathematical Institute of Russian Academy of Sciences（国立高等经济大学; 俄罗斯科学院斯特克洛夫数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对代数簇双有理自同构群中的虚拟多循环子群，证明其虚拟导出长度的上界为2d+1，曲面情形可优化为3且该界最优。
AI 中文摘要
设X是特征为零的代数闭域k上的d维代数簇，G是X的双有理自同构群Bir(X)中的一个虚拟多循环子群。我们证明G的虚拟导出长度不超过2d+1；此外，当X是曲面时，该界可改进为3，且此值是最优的。
英文摘要
Let $X$ be an algebraic variety of dimension $d$ over an algebraically closed field $k$ of zero characteristic. Suppose that $G$ is a virtually polycyclic subgroup in the group $\mathrm{Bir}(X)$ of birational automorphisms of $X$. We show that the virtual derived length of $G$ does not exceed $2d+1$. Moreover, if $X$ is a surface, the bound can be improved to $3$, and this value is optimal.
Comments12 pages; comments welcome
