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arXiv · 1809.07233

Local moduli of scalar-flat Kähler ALE surfaces

Jiyuan Han·Jeff A. Viaclovsky
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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 $\mathbb{C}^2/Γ$, where $Γ$ is a finite subgroup of ${\rm{U}}(2)$ without complex reflections, in terms of the embedding dimension of the singularity.

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Jiyuan Han, Jeff A. Viaclovsky. 2018-09-19. Local moduli of scalar-flat Kähler ALE surfaces. https://arxiv.org/abs/1809.07233

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