The Universal Kobayashi-Hitchin Correspondence on Hermitian Manifolds - Brossura

Lubke, M.; Teleman, A.

Brossura

ISBN 10: 0821839136 ISBN 13: 9780821839133

Casa editrice: Amer Mathematical Society, 2006

Riassunto

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.

Su questa edizione

• Editore: Amer Mathematical Society
• Data di pubblicazione: 2006
• ISBN 10: 0821839136
• ISBN 13: 9780821839133
• Rilegatura: Copertina flessibile
• Numero di pagine: 97