Differential Geometry Seminar: Existence and compactness theory for ALE scalar-flat Kähler surfaces

Seminar | April 8 | 3:10-4 p.m. | 939 Evans Hall

 Jiyuan Han, Purdue University

 Department of Mathematics

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. Joint with J. Viaclovsky