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arXiv · 1901.05611

Existence and compactness theory for ALE scalar-flat K\"ahler surfaces

Jiyuan Han·Jeff A. Viaclovsky
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Abstract

Our main result in this article is a compactness result which states that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat K\"ahler metrics on a minimal K\"ahler surface whose K\"ahler classes stay in a compact subset of the interior of the K\"ahler cone must have a convergent subsequence. As an application, we prove the existence of global moduli spaces of scalar-flat K\"ahler ALE metrics for several infinite families of K\"ahler ALE spaces.

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Jiyuan Han, Jeff A. Viaclovsky. 2019-01-17. Existence and compactness theory for ALE scalar-flat K\"ahler surfaces. https://doi.org/10.1017/fms.2019.42

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