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A remark on polycyclic groups of birational automorphisms
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 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.
Related
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BibTeX
@misc{golota2026remark,
title = {{A remark on polycyclic groups of birational automorphisms}},
author = {Aleksei Golota},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.31086},
eprint = {2608.31086},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.31086},
}
RIS
TY - UNPB
TI - A remark on polycyclic groups of birational automorphisms
AU - Aleksei Golota
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2608.31086
UR - https://arxiv.org/abs/2608.31086
AB - 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 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.
ER -