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...

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Bibliographic Details
Main Author: Aust, Holger
Contributors: Schumacher, Georg (Prof. Dr.) (Thesis advisor)
Format: Doctoral Thesis
Published: Philipps-Universität Marburg 2009
Online Access:PDF Full Text
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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.