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Transactions of the American Mathematical Society

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Tame sets, dominating maps, and complex tori

Author: Gregery T. Buzzard
Journal: Trans. Amer. Math. Soc. 355 (2003), 2557-2568
MSC (2000): Primary 32H02; Secondary 32E30
Published electronically: December 18, 2002
MathSciNet review: 1974003
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Abstract: A discrete subset of $\mathbb C^n$ is said to be tame if there is an automorphism of $\mathbb C^n$ taking the given discrete subset to a subset of a complex line; such tame sets are known to allow interpolation by automorphisms. We give here a fairly general sufficient condition for a discrete set to be tame. In a related direction, we show that for certain discrete sets in $\mathbb C^n$ there is an injective holomorphic map from $\mathbb C^n$ into itself whose image avoids an $\epsilon$-neighborhood of the discrete set. Among other things, this is used to show that, given any complex $n$-torus and any finite set in this torus, there exist an open set containing the finite set and a locally biholomorphic map from $\mathbb C^n$ into the complement of this open set.

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Additional Information

Gregery T. Buzzard
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907

Received by editor(s): June 20, 1999
Published electronically: December 18, 2002
Additional Notes: Supported in part by an NSF Postdoctoral Fellowship
Article copyright: © Copyright 2002 American Mathematical Society

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