Hyperpolygon spaces: beyond the movable cone

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