108. Immanuel van Santen A Characterization of Rationality and Borel Subgroups

This is joint work with Andriy Regeta and Christian Urech. In this talk, we focus on the following two questions about the group of birational transformations, Bir(X), of an irreducible variety X: 1. If Bir(X) and Bir(P^n) are isomorphic, does this imply that X and P^n are birational? 2. What are the Borel subgroups of Bir(X)? The first question was answered affirmatively in 2014 by Serge Cantat under the additional assumption that dim X = 2 (the case n = 2 was treated by Furter and Hedén). This answers affirmatively a conjecture of Vladimir Popov.