EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES
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 s...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2020-01-01
|
| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509419000422/type/journal_article |
| _version_ | 1811156204932562944 |
|---|---|
| author | JIYUAN HAN JEFF A. VIACLOVSKY |
| author_facet | JIYUAN HAN JEFF A. VIACLOVSKY |
| author_sort | JIYUAN HAN |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T04:47:36Z |
| format | Article |
| id | doaj.art-d557783921d8409a8f5850270f95599f |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-04-10T04:47:36Z |
| publishDate | 2020-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-d557783921d8409a8f5850270f95599f2023-03-09T12:34:47ZengCambridge University PressForum of Mathematics, Sigma2050-50942020-01-01810.1017/fms.2019.42EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACESJIYUAN HAN0JEFF A. VIACLOVSKY1Department of Mathematics, Purdue University, West Lafayette, IN, 47907, USA;Department of Mathematics, University of California, Irvine, CA, 92697, USA;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.https://www.cambridge.org/core/product/identifier/S2050509419000422/type/journal_article53C5553C25 |
| spellingShingle | JIYUAN HAN JEFF A. VIACLOVSKY EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES Forum of Mathematics, Sigma 53C55 53C25 |
| title | EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES |
| title_full | EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES |
| title_fullStr | EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES |
| title_full_unstemmed | EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES |
| title_short | EXISTENCE AND COMPACTNESS THEORY FOR ALE SCALAR-FLAT KÄHLER SURFACES |
| title_sort | existence and compactness theory for ale scalar flat kahler surfaces |
| topic | 53C55 53C25 |
| url | https://www.cambridge.org/core/product/identifier/S2050509419000422/type/journal_article |
| work_keys_str_mv | AT jiyuanhan existenceandcompactnesstheoryforalescalarflatkahlersurfaces AT jeffaviaclovsky existenceandcompactnesstheoryforalescalarflatkahlersurfaces |