English

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

Differential Geometry 2020-02-19 v2 Algebraic Geometry

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.

Keywords

Cite

@article{arxiv.1901.05611,
  title  = {Existence and compactness theory for ALE scalar-flat K\"ahler surfaces},
  author = {Jiyuan Han and Jeff A. Viaclovsky},
  journal= {arXiv preprint arXiv:1901.05611},
  year   = {2020}
}

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50 pages