局部自同态群的可解长度
The solvable length of groups of local diffeomorphisms
摘要：
我们感兴趣的是局部双全纯群的代数性质及其结果。一个自然的问题是可解群的复杂性是否受周围空间的维数限制。在这种精神下，我们表明，$2n+1$是最尖锐的上界导出长度的可解子群的组$\mathrm{Diff}({\mathbb C}^{n},0)$的局部复杂的解析同构$n=2,3,4,5$。
英文摘要：
We are interested in the algebraic properties of groups of local biholomorphisms and their consequences. A natural question is whether the complexity of solvable groups is bounded by the dimension of the ambient space. In this spirit we show that $2n+1$ is the sharpest upper bound for the derived length of solvable subgroups of the group $\mathrm{Diff}({\mathbb C}^{n},0)$ of local complex analytic diffeomorphisms for $n=2,3,4,5$.
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