The solvable length of groups of local diffeomorphisms

Abstract

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 $n=2,3,4,5$.

40 pages, Accepted for publication in Journal für die reine und angewandte Mathematik

References in corpus (1)

• Recurrent orbits of subgroups of local complex analytic diffeomorphisms

Cited by in corpus (2)

• Finite dimensional groups of local diffeomorphisms
• Boundness of intersection numbers for actions by two-dimensional biholomorphisms