The universal Kobayashi-Hitchin correspondence on Hermitian manifolds

Details The universal Kobayashi-Hitchin correspondence on Hermitian manifolds The universal Kobayashi-Hitchin correspondence on Hermitian manifolds

2004-02-21

arxiv.org/abs/math/0402341v4

Mathematics

Differential Geometry

LaTeX, 90 pages, March 12 2004: Revised version; Corrections of minor nature; Comments are welcome March 2005: New revised ver

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The universal Kobayashi-Hitchin correspondence on Hermitian manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The universal Kobayashi-Hitchin correspondence on Hermitian manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The universal Kobayashi-Hitchin correspondence on Hermitian manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-221540