Toric degenerations of partial flag varieties via matching fields and combinatorial mutations

Abstract: Toric degenerations are an important tool that can be used to analyze algebraic varieties as they allow us to understand a general variety via the geometry of their associated toric varieties. In this talk, I will show how to produce a new large family of toric degenerations of Grassmannians and (partial) flag varieties, whose combinatorics is governed by matching fields. Moreover, I will study the relations between polytopes associated to different toric degenerations of the same variety. This is done using the tool of combinatorial mutations, particular piecewise linear functions on polytopes. Finally, I will show how our methods can be used to compute new families of toric degenerations of small Grassmannians and flag varieties. This talk is based on joint work with Oliver Clarke and Fatemeh Mohammadi.

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