Introduced by Konno, hyperpolygon spaces are examples of Nakajima quiver varieties. The simplest of these is a noncompact complex surface admitting the structure of a gravitational instanton, and therefore fits nicely into the Kronheimer-Nakajima classification of complete ALE hyperkaehler 4-manifolds, which is a geometric realization of the McKay correspondence for finite subgroups of SU(2). For more general hyperpolygon spaces, we can speculate on how
this classification might be extended by studying the geometry of hyperpolygons at "infinity". This is ongoing work with Hartmut Weiss.
- Geometry and Analysis Seminar