Actions of connected algebraic groups on rational 3-dimensional Mori fibrations

Abstract: In this talk we will study the connected algebraic groups acting on Mori fibrations $X \to Y$ with $X$ a rational threefold and $Y$ a curve or a surface. We will see how these groups can be classified, using the minimal model program (MMP) and the Sarkisov program, and how our results make possible to recover most of the classification of the connected algebraic subgroups of the Cremona group $\mathrm{Bir}(\mathbb{P}^3)$ obtained by Hiroshi Umemura in the 1980's when the base field is the field of complex numbers.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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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

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