Constructing Laurent polynomial mirrors for quiver flag zero loci
Elana Kalashnikov (Harvard)
Abstract: All smooth Fano varieties of dimension at most three can be constructed as either toric complete intersections (subvarieties of toric varieties) or quiver flag zero loci (subvarieties of quiver flag varieties). Conjecturally, Fano varieties are expected to mirror certain Laurent polynomials. The construction of mirrors of Fano toric complete intersections is well-understood. In this talk, I'll discuss evidence for this conjecture by proposing a method of constructing mirrors for Fano quiver flag zero loci. A key step of the construction is via finding toric degenerations of the ambient quiver flag varieties. These degenerations generalise the Gelfand-Cetlin degeneration of flag varieties, which in the Grassmannian case has an important role in the cluster structure of its coordinate ring.
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
| Organizers: | Alexander Kasprzyk*, Johannes Hofscheier*, Erroxe Etxabarri Alberdi |
| *contact for this listing |