Year: 2024
Type: preprint
Abstract: Let X be an irreducible variety and Bir(X) its group of birational transformations. We show that the group structure of Bir(X) determines whether X is rational and whether X is ruled. Additionally, we prove that any Borel subgroup of Bir(X) has derived length at most twice the dimension of X, with equality occurring if and only if X is rational and the Borel subgroup is standard. We also provide examples of non-standard Borel subgroups of Bir(P^n) and Aut(A^n), thereby resolving conjectures by Popov and Furter-Poloni.
Source: arXiv (Cornell University)
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4403663357