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EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES

Published online by Cambridge University Press:  10 January 2020

JIYUAN HAN
Affiliation:
Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA; [email protected]
JEFF A. VIACLOVSKY
Affiliation:
Department of Mathematics, University of California, Irvine, CA, 92697, USA; [email protected]

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.

Type
Differential Geometry and Geometric Analysis
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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