Local moduli of scalar-flat Kähler ALE surfaces

Abstract

In this article, we give a survey of our construction of a local moduli space of scalar-flat Kähler ALE metrics in complex dimension $2$. We also prove an explicit formula for the dimension of this moduli space on a scalar-flat Kähler ALE surface which deforms to the minimal resolution of ${\mathbb{C}}^2/\Gamma$, where $\Gamma$ is a finite subgroup of $\mathrm{U}(2)$ without complex reflections, in terms of the embedding dimension of the singularity.

19 pages, contains survey of main results in arXiv:1605.05267, and also some new results