Type D associahedra are unobstructed

Nathan Ilten (Simon Fraser)

13-Aug-2020, 15:00-16:00 (4 years ago)

Abstract: Generalized associahedra associated to any root system were introduced by Fomin and Zelevinsky in their study of cluster algebras. For type $\mathsf{A}$ root systems, one recovers the classical associahedron parametrizing triangulations of a regular $n$-gon. For type $\mathsf{D}$ root systems, one obtains a polytope parametrizing centrally symmetric triangulations of a $2n$-gon. In previous work, Jan Christophersen and I showed that the Stanley-Reisner ring of the simplicial complex dual to the boundary of the classical associahedron is unobstructed, that is, has vanishing second cotangent cohomology. This could be used to find toric degenerations of the Grassmannian $\mathrm{Gr}(2,n)$. In this talk, I will describe work-in-progress that generalizes this unobstructedness result to the type $\mathsf{D}$ associahedron.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )


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

Organizers: Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi
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