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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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| Materialtyp: | Dissertation |
| Språk: | engelska |
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Philipps-Universität Marburg
2009
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| Länkar: | PDF-fulltext |
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| Sammanfattning: | 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. |
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| Fysisk beskrivning: | 84 Seiten |
| DOI: | 10.17192/z2010.0073 |