Large Discrete Sets in Stein manifolds

Joerg Winkelmann

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arXiv · math/9808087

Large Discrete Sets in Stein manifolds

Joerg Winkelmann

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Abstract

Rosay and Rudin constructed examples of discrete subsets of C^n with remarkable properties. We generalize these constructions from C^n to arbitrary Stein manifolds. We prove: Given a Stein manifold X and a affine variety V of the same dimension there exists a discrete subset D in X such that (1) X-D is measure hyperbolic, (2) f(V) intersects D for every non-degenerate holomorphic map from V to X and (3) every automorphism of X preserving the set D is already the identity map. We also give examples which demonstrate that such discrete subsets can not be found in arbitrary non-Stein manifolds.

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BibTeX RIS

Joerg Winkelmann. 1998-08-19. Large Discrete Sets in Stein manifolds. https://arxiv.org/abs/math/9808087

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