Hyperpolygon spaces and their cores

Given an nn-tuple of positive real numbers (α1,…,αn)(\alpha _1,\ldots ,\alpha _n), Konno (2000) defines the hyperpolygon space X(α)X(\alpha ), a hyperkähler analogue of the Kähler variety M(α)M(\alpha ) parametrizing polygons in R3\mathbb {R}^3 with edge lengths (α1,…,αn)(\alpha _1,\ldots ,\alpha _n). The polygon space M(α)M(\alpha ) can be interpreted as the moduli space of stable representations of a certain quiver with fixed dimension vector;…