The universal Kobayashi-Hitchin correspondence on Hermitian manifolds
Author(s)
Bibliographic Information
The universal Kobayashi-Hitchin correspondence on Hermitian manifolds
（Memoirs of the American Mathematical Society, no. 863）
American Mathematical Society, 2006
Available at 14 libraries
Note
"Volume 183, number 863 (third of 4 numbers)."
Includes bibliographical references (p. 95-97)
Description and Table of Contents
Description
We prove a very general Kobayashi-Hitchin correspondence on arbitrary compact Hermitian manifolds, and we discuss differential geometric properties of the corresponding moduli spaces. 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. Using ideas from Donaldson theory, we further introduce and investigate canonical Hermitian metrics on such moduli spaces. We discuss in detail remarkable classes of moduli spaces in the non-Kahlerian framework: Oriented holomorphic structures, Quot-spaces, oriented holomorphic pairs and oriented vortices, non-abelian Seiberg-Witten monopoles.
Table of Contents
Introduction The finite dimensional Kobayashi-Hitchin correspondence A ""universal"" complex geometric classification problem Hermitian-Einstein pairs Polystable pairs allow Hermitian-Einstein reductions Examples and applications Appendix Bibliography.
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