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Hyperbolizität in der komplexen Analysis und der algebraischen Geometrie
In dieser Arbeit werden ganze Abbildungen in den projektiven Raum betrachtet, die mehrkomponentige Hyperflächen bestimmten Grades meiden, und es wird deren algebraische Entartung bzw. Konstanz gezeigt. Hauptresultat ist der Beweis eines Spezialfalls der Kobayashi-Vermutung, nämlich der Nachweis der...
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| Format: | Doctoral Thesis |
| Language: | German |
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Philipps-Universität Marburg
2006
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| Online Access: | PDF Full Text |
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In this thesis, we consider entire mappings into projective space which omit hypersurfaces with several components of a certain degree and we show that they are algebraically degenerate or even constant. The main result is the proof of a special case of Kobayashi's conjecture, namely the proof of the hyperbolicity of the complement of a six component surface of degree seven in three-dimensional projective space (as well as that of a surface with five components none of which is a plane). This is achieved very directly using elementary methods such as Brody's reparametrization lemma.