Symmetries of Fano varieties

Abstract: Prokhorov and Shramov showed that the BAB conjecture (later proven by Birkar) implies the Jordan property for automorphism groups of complex Fano varieties. This property in particular gives an upper bound on the size of semisimple groups acting faithfully on $n$-dimensional complex Fano varieties, and this bound only depends on $n$. We investigate the geometric consequences of an action by a large semisimple group - in particular the symmetric group. We give an effective upper bound on the size of these symmetric group actions, and we obtain optimal bounds for certain classes of varieties (toric varieties and Fano weighted complete intersections). Finally, we draw a connection between large symmetric actions and boundedness of varieties, by showing that the maximally symmetric Fano fourfolds form a bounded family. This work is joint with Louis Esser and Joaquín Moraga.

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