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...

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Bibliographic Details
Main Author: Stemmler, Matthias
Contributors: Schumacher, Georg (Prof. Dr.) (Thesis advisor)
Format: Dissertation
Language:English
Published: Philipps-Universität Marburg 2009
Reine und Angewandte Mathematik
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Summary: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.
DOI:https://doi.org/10.17192/z2010.0073