Rigid birational involutions of $\mathbb{P}^3$ and cubic threefolds
Algebraic Geometry
2023-01-20 v3
Abstract
We construct families of birational involutions on or a smooth cubic threefold which do not fit into a non-trivial elementary relation of Sarkisov links. As a consequence, we construct new homomorphisms from their group of birational transformations, effectively re-proving their non-simplicity. We also prove that these groups admit a free product structure. Finally, we produce automorphisms of these groups that are not generated by inner and field automorphisms.
Keywords
Cite
@article{arxiv.2111.04711,
title = {Rigid birational involutions of $\mathbb{P}^3$ and cubic threefolds},
author = {Sokratis Zikas},
journal= {arXiv preprint arXiv:2111.04711},
year = {2023}
}
Comments
minor revisions, final version, to appear in Journal de l'\'Ecole polytechnique, 18 pages