Date/heure
27 janvier 2025
14:00 - 15:00
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Christian Urech
Catégorie d'évènement Séminaire de géométrie complexe
Résumé
To an algebraic variety X we associate its group of birational transformations Bir(X). In this talk, we will see the following theorem: If X is an algebraic variety such that Bir(X) is isomorphic to Bir(P^n), where P^n is the n-dimensional projective space, then X is birational to P^n. In other words, the group structure of Bir(X) determines whether X is rational or not. In another direction, I will explain that Borel subgroups of Bir(X), i.e. maximal connected solvable subgroups, are of derived length <= 2 dim(X) with equality if and only if X is rational and the Borel subgroup is standard. This is joint work with Regeta and Van Santen.