Combinatorial mutations and block diagonal polytopes

Abstract: Matching fields were introduced by Sturmfels and Zelevinsky to study certain Newton polytopes and more recently have been shown to give rise to toric degenerations of various families of varieties. Whenever a matching field gives rise to a toric degeneration of the Grassmannian, the polytope of the associated toric variety coincides with the matching field polytope. In this talk I will describe combinatorial mutations of matching field polytopes. We will explore properties of polytopes which are preserved by mutation, and we will see that property of giving rise to a toric degeneration is preserved by mutations. This gives us an easy way to generate new families of toric degenerations of the Grassmannian from old. This talk is based on joint work with Akihiro Higashitani 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