Hyperkähler Degenerations from Parabolic $\mathrm{SL}(2,\mathbb{C})$-Higgs Bundles Moduli Spaces on the Punctured Sphere to Hyperpolygon Spaces

Laura Fredrickson, Arya Yae

Complete hyperkähler 4-manifolds of finite energy are grouped into ALE, ALF, ALG${}^{(\ast )}$, ALH${}^{(\ast )}$, each of these being further classified according to the Dynkin type of their…