Stability and Hermitian-Einstein metrics for vector bundles on framed manifolds
The notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles are adapted for canonically polarized framed manifolds, i. e. compact complex manifolds together with a smooth divisor admitting a certain projective e...
Gespeichert in:
1. Verfasser: | |
---|---|
Beteiligte: | |
Format: | Dissertation |
Sprache: | Englisch |
Veröffentlicht: |
Philipps-Universität Marburg
2009
|
Schlagworte: | |
Online Zugang: | PDF-Volltext |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
Zusammenfassung: | The notions of stability of holomorphic vector bundles in the sense of Mumford-Takemoto and Hermitian-Einstein metrics in holomorphic vector bundles are adapted for canonically polarized framed manifolds, i. e. compact complex manifolds together with a smooth divisor admitting a certain projective embedding. The main tool is the Poincaré metric, a special complete Kähler-Einstein metric on the complement of the divisor, whose asymptotic behaviour near the divisor is well-known due to results by Schumacher. The existence and uniqueness of Hermitian-Einstein connections in stable holomorphic vector bundles (Kobayashi-Hitchin correspondence) is proved in the setting of framed manifolds. |
---|---|
Umfang: | 84 Seiten |
DOI: | 10.17192/z2010.0073 |