Approximate Hitchin-Kobayashi correspondence for Higgs \(G\)-bundles (Q2925084)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Approximate Hitchin-Kobayashi correspondence for Higgs \(G\)-bundles |
scientific article; zbMATH DE number 6359094
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximate Hitchin-Kobayashi correspondence for Higgs \(G\)-bundles |
scientific article; zbMATH DE number 6359094 |
Statements
20 October 2014
0 references
principal Higgs bundles
0 references
semistability
0 references
approximate Hermitian-Yang-Mills structures
0 references
Hermitian-Yang-Mills metrics
0 references
0 references
0 references
0 references
Approximate Hitchin-Kobayashi correspondence for Higgs \(G\)-bundles (English)
0 references
A Hitchin-Kobayashi correspondence for vector bundles equipped with a Higgs field was established by \textit{C. T. Simpson} [J. Am. Math. Soc. 1, No. 4, 867--918 (1988; Zbl 0669.58008)]. In [J. Reine Angew. Math. 612, 59--79 (2007; Zbl 1138.14024)], \textit{U. Bruzzo} and \textit{B. G. Otero} proved that Higgs vector bundles that carry an approximate Hermitian-Yang-Mills (HYM) structure are semistable, while the opposite implication is due to \textit{S. A. H. Cardona} [Ann. Global Anal. Geom. 42, No. 3, 349--370 (2012; Zbl 1260.58006); ibid. 44, No. 4, 455--469 (2013; Zbl 1303.58012)]. In this paper the existence of an approximate Hitchin-Kobayashi correspondence for principal Higgs bundles is announced.
0 references
