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EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES

Part of: Global differential geometry

Published online by Cambridge University Press:  10 January 2020

JIYUAN HAN  and
JEFF A. VIACLOVSKY
JIYUAN HAN
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA; han556@purdue.edu
JEFF A. VIACLOVSKY
Affiliation:
Department of Mathematics, University of California, Irvine, CA, 92697, USA; jviaclov@uci.edu

Abstract

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

MSC classification

Primary: 53C55: Hermitian and Kählerian manifolds
Secondary: 53C25: Special Riemannian manifolds (Einstein, Sasakian, etc.)
Type
Differential Geometry and Geometric Analysis
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e1
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2020

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