Complex Analysis seminar (25. February 2025)
Date: 25 February 2025, 12:30
Room: 3.05 (Complex Analysis Seminar)
Speaker: Immanuel van Santen (University of Bern)
Title: The group of birational transformations detects rationality
Abstract: This is joint work with Andriy Regeta (University of Jena/Padova) and Christian Urech (ETH Zürich). We investigate whether the group of birational transformations, Bir(X), of an irreducible variety X detects rationality. Specifically, if Bir(X) is isomorphic to Bir(P^n), does it follow that X and P^n are birationally equivalent? For varieties X of dimension at most n, this question was affirmatively answered by Serge Cantat in 2014. In this talk, I will provide an overview of the techniques that ultimately lead to a positive resolution of this question in all dimensions and outline the main ideas of the proof. If time permits, I will also discuss our latest results concerning Borel subgroups in Bir(X), which lead to another group-theoretical characterization of rationality.
