Large Discrete Sets in Stein Manifolds
Jörg Winkelmann
Abstract.
Rosay and Rudin constructed examples of discrete subsets of
Cn with remarkable properties. We generalize these constructions
from Cn 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
-
X-D is measure hyperbolic,
- f(V) intersects D for every non-degenerate
holomorphic map f from V to X and
- 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.
Appeared in:
Mathematischen Zeitschrift .
236, (4), 883-901 (2001)
Related later work:
Tameness and growth conditions.
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Last modification: 31 March 2008