Equivariant geometry of quadric bundles and maximal subgroups of Cremona groups

par Sokratis Zikas (Université de Poitiers)

jeudi 12 oct. 2023, 10:30 → 12:30 Europe/Paris

Maximal connected algebraic subgroups of the group of birational transformations Bir(X) of a variety $X$ appear as automorphism groups of Mori fiber spaces birational to $X$. When $X={\mathbb{P}}^n$, for $n=2$ or $3$ we have a classification of such groups and the models they act on, while in dimension 4 and more this is an open problem. In this talk we will explore the equivariant geometry of a class of quadric fibrations over ${\mathbb{P}}^1$. As a result, we will see how their automorphism groups gives us families of maximal subgroups of $Bir({\mathbb{P}}^n)$ for any $n$ at least 4. This is work in progress, joint with Enrica Floris.