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arXiv · 2409.07864

Group Theoretical Characterizations of Rationality

Andriy Regeta·Christian Urech·Immanuel van Santen
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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.

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Andriy Regeta, Christian Urech, Immanuel van Santen. 2024-09-12. Group Theoretical Characterizations of Rationality. https://arxiv.org/abs/2409.07864

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