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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Approximation of holomorphic maps with a lower bound on the rank


Author: Dejan Kolaric
Journal: Proc. Amer. Math. Soc. 136 (2008), 1273-1284
MSC (2000): Primary 32E30, 32H02, 32M17, 32Q28
Published electronically: December 28, 2007
MathSciNet review: 2367101
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Abstract: Let $ K$ be a closed polydisc or ball in $ \mathbb{C}^n$, and let $ Y$ be a quasi-projective algebraic manifold which is Zariski locally equivalent to $ \mathbb{C}^p$, or a complement of an algebraic subvariety of codimension $ \ge 2$ in such a manifold. If $ r$ is an integer satisfying $ (n-r+1) (p-r+1)\geq 2$, then every holomorphic map from a neighborhood of $ K$ to $ Y$ with rank $ \ge r$ at every point of $ K$ can be approximated uniformly on $ K$ by entire maps $ \mathbb{C}^n\to Y$ with rank $ \ge r$ at every point of $ \mathbb{C}^n$.


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Additional Information

Dejan Kolaric
Affiliation: Institute of Mathematics, Physics and Mechanics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia
Email: dejan.kolaric@fmf.uni-lj.si

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08956-3
PII: S 0002-9939(07)08956-3
Keywords: Holomorphic maps, approximation, transversality, algebraic sets
Received by editor(s): June 9, 2006
Received by editor(s) in revised form: December 5, 2006
Published electronically: December 28, 2007
Additional Notes: Work on this paper was supported by ARRS, Republic of Slovenia.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.