Rigid birational involutions of ℙ³ and cubic threefolds

2021/11/08 by Sokratis Zikas, Zikas, Sokratis
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.2111.04711

Abstract

We construct families of birational involutions on ℙ³ 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.

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