On connected algebraic subgroups of groups of birational transformations

Abstract: The problem of understanding the structure of the group of birational transformations $\mathrm{Bir}(X)$ of a projective variety $X$ is an old one, with early results dating all the way back to the 19th century. In general $\mathrm{Bir}(X)$ does not admit the structure of an algebraic group; however one may study algebraic subgroups of it and how they relate to one another. In the last decade there has been a resurgence of results in this area, mainly due to the use of the modern machinery of the Minimal Model Program and the Sarkisov Program. In this talk I will present this modern framework as well as various results around the study of algebraic subgroups of $\mathrm{Bir}(X)$ for a Mori fiber space $X$.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html