Rigid birational involutions of \(\mathbb{P}^3\) and cubic threefolds. (Involutions birationnelles rigides de \(\mathbb{P}^3\) et de cubiques lisses de dimension \(3\).) (English. French summary) Zbl 1506.14033
Summary: We construct families of birational involutions on \(\mathbb{P}^3\) or on 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.
MSC:
| 14E07 | Birational automorphisms, Cremona group and generalizations |
| 14E05 | Rational and birational maps |
| 14E30 | Minimal model program (Mori theory, extremal rays) |
References:
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