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Embeddings through discrete sets of balls

Stefan Borell Institute of Mathematics, University of Berne Frank Kutzschebauch Institute of Mathematics, University of Berne

TBD mathscidoc:1701.333135

Arkiv for Matematik, 46, (2), 251-269, 2006.12
We investigate whether a Stein manifold$M$which allows proper holomorphic embedding into ℂ^{$n$}can be embedded in such a way that the image contains a given discrete set of points and in addition follow arbitrarily close to prescribed tangent directions in a neighbourhood of the discrete set. The infinitesimal version was proven by Forstnerič to be always possible. We give a general positive answer if the dimension of$M$is smaller than$n$/2 and construct counterexamples for all other dimensional relations. The obstruction we use in these examples is a certain hyperbolicity condition.
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@inproceedings{stefan2006embeddings,
  title={Embeddings through discrete sets of balls},
  author={Stefan Borell, and Frank Kutzschebauch},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203623435918944},
  booktitle={Arkiv for Matematik},
  volume={46},
  number={2},
  pages={251-269},
  year={2006},
}
Stefan Borell, and Frank Kutzschebauch. Embeddings through discrete sets of balls. 2006. Vol. 46. In Arkiv for Matematik. pp.251-269. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203623435918944.
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