Connected algebraic groups acting on Fano fibrations over P^1

Abstract: Let $G$ be a connected algebraic group and $X$ a variety endowed with a regular action of $G$ and a Mori fibre space $X/\mathbb P^1$ whose fibre is a Fano variety of Picard rank at least 2. In this talk I will explain why there is a proper horizontal subvariety of $X$ which is invariant under the action of $G$, alongside with some applications of this result to the classification of connected algebraic subgroups of the Cremona group in dimension 4. This is a joint work with Jérémy Blanc.

algebraic geometryalgebraic topologycomplex variablesdifferential geometrygeometric topologymetric geometryquantum algebrarepresentation theory

Audience: researchers in the topic

Sapienza A&G Seminar

Series comments: Weekly research seminar in algebra and geometry.

"Sapienza" Università di Roma, Department of Mathematics "Guido Castelnuovo".