Rigid birational involutions of ${\mathbb{P}}^3$ and cubic threefolds

Abstract

We construct families of birational involutions on ${\mathbb{P}}^3$ 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.

minor revisions, final version, to appear in Journal de l'École polytechnique, 18 pages

References in corpus (1)

• Quotients of higher dimensional Cremona groups