Buildings as classifying spaces for toric principal bundles

Abstract: A building is a certain infinite combinatorial object (abstract simplicial complex) associated to a (semisimple) linear algebraic group which encodes the relative position of maximal tori and parabolic/parahoric subgroups in it. After an introduction to buildings and discussing some examples from linear algebra, I will talk about some recent results on classification of torus equivariant principal G-bundles on toric varieties (over a field) and toric schemes (over a discrete valuation ring). These are extensions of Klyachko's classification of torus equivariant vector bundles on toric varieties. For this we introduce the notions of "piecewise linear map" to the Tits building and "piecewise affine map" to the Bruhat-Tits building of a linear algebraic group. This is joint work with Chris Manon (Kentucky) and Boris Tsvelikhovsky (Pittsburgh).

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