Fano spherical varieties of small dimension and rank

Abstract: A spherical variety $(X,G)$ is a normal complex algebraic variety $X$ equipped with the action of a connected complex reductive group $G$ such that a Borel subgroup $B$ of $G$ acts with an open dense orbit. The rank of $(X,G)$ is the rank of the lattice of $B$-eigenvalues in the $B$-module of rational functions on $X$. I will present the classification of the 260 locally factorial Fano spherical varieties $(X,G)$ of dimension four and of rank two or less, obtained in a joint work with Pierre-Louis Montagard. Those spherical varieties are described via combinatorial data, from which it is easy to read off geometric properties of the underlying variety $X$, such as the Picard rank, anticanonical degree, K-stability, etc.

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