The universal Kobayashi-Hitchin correspondence on Hermitian manifolds
By M. Lubke, A. Teleman. 2004
75 citations recorded by the source corpus.
We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds. This correspondence refers to moduli spaces of "universal holomorphic oriented pairs". Most of the classical moduli problems in complex geometry (e. g. holomorphic bundles with reductive structure groups, holomorphic pairs, holomorphic Higgs pairs, Witten triples, arbitrary quiver moduli problems) are special cases of this universal classification problem. Our Kobayashi-Hitchin correspondence relates the complex geometric concept "polystable oriented holomorphic pair" to the existence of a reduction solving a generalized Hermitian-Einstein equation. The proof is based on the Uhlenbeck-Yau continuity method. We also investigate metric properties of the moduli spaces in this general non-Kaehlerian framework. We discuss in more detail moduli spaces of oriented connections, Douady Quot spaces and moduli spaces of non-abelian monopoles.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/415d95cee0e3ab256c961e0e89ac225d07168a10
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Kobayashi-Hitchin correspondence for tame harmonic bundles II (2006, background): “We do not recall history or background about the study of KobayashiHitchin correspondence and harmonic bundles, for which we refer to the introductions of [38], [24] or [31], for example.”
- Moduli for decorated tuples of sheaves and representation spaces for quivers (2004, unknown): “Keywords: Quiver, representation, decoration, split sheaf, moduli space, Hitchin map.”