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arXiv · 2608.31086

A remark on polycyclic groups of birational automorphisms

Aleksei Golota
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Abstract

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.

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Aleksei Golota. 2026-08-31. A remark on polycyclic groups of birational automorphisms. https://arxiv.org/abs/2608.31086

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