Embeddings through discrete sets of balls |
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Authors: | Stefan Borell Frank Kutzschebauch |
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Affiliation: | (1) Institute of Mathematics, University of Berne, Sidlerstrasse 5, CH-3012 Berne, Switzerland |
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Abstract: | 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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