Photo by austindistel from unsplash
In this article, we give an analytic construction of ALF hyperkähler metrics on smooth deformations of the Kleinian singularity $\mathbb{C}^{2}/{\mathcal{D}}_{k}$ , with ${\mathcal{D}}_{k}$ the binary dihedral group of order $4k$… Click to show full abstract
In this article, we give an analytic construction of ALF hyperkähler metrics on smooth deformations of the Kleinian singularity $\mathbb{C}^{2}/{\mathcal{D}}_{k}$ , with ${\mathcal{D}}_{k}$ the binary dihedral group of order $4k$ , $k\geqslant 2$ . More precisely, we start from the ALE hyperkähler metrics constructed on these spaces by Kronheimer, and use analytic methods, e.g. resolution of a Monge–Ampère equation, to produce ALF hyperkähler metrics with the same associated Kähler classes.
Journal Title: Compositio Mathematica
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!