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Einbettung von quasi-projektiven Mannigfaltigkeiten und effektive Resultate
In dieser Arbeit werden Geradenbündel, welche auf einer Zariski-offenen Teilmenge einer projektiven Mannigfaltigkeiten gewisse Positivitätseigenschaften besitzt, im Hinblick auf die Einbettung eben dieser Teilmenge in den komplexen projektiven Raum betrachtet. Als Positivitätseigenschaft benötigen w...
| Príomhchruthaitheoir: | |
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| Rannpháirtithe: | |
| Formáid: | Dissertation |
| Teanga: | Gearmáinis |
| Foilsithe / Cruthaithe: |
Philipps-Universität Marburg
2009
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| Ábhair: | |
| Rochtain ar líne: | An téacs iomlán mar PDF |
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In this thesis, we consider line bundles, which possess some positivity conditions on a Zariski-open subset of a projective manifold, to embed the subset in complex projective space. As the positivity condition we need the existence of a singular hermitian metric, which has positive curvature and vanishing Lelong-number on the inside of the projective manifold. Then the Zariski-open subset can be embedded with the help of a multiple of the canonical bundle and a multiple of the line bundle, which is singular-positive modulo boundary. Furthermore we achieve an effective result for the jet-generation in isolated points, i.e. we can bound the multiplicity of the canonical bundle to 2 and construct an explicit bound, only dependend on the dimension of the underlying manifold, the number of points and the jet-order in those points, for the multiplicity of the singular-positive line bunde.