The Universal Kobayashi Hitchin Correspondence on Hermitian Manifolds is popular PDF and ePub book, written by Martin Lübke in 2006, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, The Universal Kobayashi Hitchin Correspondence on Hermitian Manifolds can be Read Online from any device for your convenience.
The Universal Kobayashi Hitchin Correspondence on Hermitian Manifolds Book PDF Summary
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.
Detail Book of The Universal Kobayashi Hitchin Correspondence on Hermitian Manifolds PDF
- Author : Martin Lübke
- Release : 19 September 2024
- Publisher : American Mathematical Soc.
- ISBN : 9780821839133
- Genre : Mathematics
- Total Page : 112 pages
- Language : English
- PDF File Size : 12,9 Mb
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