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Embeddings through Discrete Sets of Discs
University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.
University of Berne Institute of Mathematics Sidlerstrasse 5 CH-3012 Berne Switzerland.
2008 (English)In: Arkiv för matematik, ISSN 0004-2080, E-ISSN 1871-2487, Vol. 46, no 2, 251-269 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2008. Vol. 46, no 2, 251-269 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:miun:diva-15026DOI: 10.1007/s11512-008-0079-8OAI: oai:DiVA.org:miun-15026DiVA: diva2:461584
Available from: 2011-12-05 Created: 2011-12-05 Last updated: 2011-12-08Bibliographically approved

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Borell, StefanKutzschebauch, Frank
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