Hyperpolygon spaces: beyond the movable cone
Alastair Craw (Bath)
Abstract: For $n\geq 4$, the hyperpolygon spaces are a collection of Nakajima quiver varieties in dimension $2n-6$ that have been a useful testing ground for conjectures on conical symplectic varieties. I'll describe joint work in progress with Gwyn Bellamy, Steven Rayan, Travis Schedler and Hartmut Weiss in which we describe completely the birational geometry of these spaces. The case $n=5$ recovers a well-known finite quotient singularity in dimension four, and allows us to provide a uniform construction of all 81 projective crepant resolutions studied in previous work of Donten-Bury--Wi\'{s}niewski. I'll also explain the title of the talk by giving a geometric interpretation of the components of the stability parameter even when it doesn't lie in the positive orthant.
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 |