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

DOI:
https://doi.org/10.1090/S0002-9947-02-03229-4

Published electronically:
December 18, 2002

MathSciNet review:
1974003

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Abstract: A discrete subset of is said to be tame if there is an automorphism of 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 there is an injective holomorphic map from into itself whose image avoids an -neighborhood of the discrete set. Among other things, this is used to show that, given any complex -torus and any finite set in this torus, there exist an open set containing the finite set and a locally biholomorphic map from 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

Email:
buzzard@math.purdue.edu

DOI:
https://doi.org/10.1090/S0002-9947-02-03229-4

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