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

 

Degree of a holomorphic map between unit balls from $ \mathbb{C}^2$ to $ \mathbb{C}^n$


Author: Francine Meylan
Journal: Proc. Amer. Math. Soc. 134 (2006), 1023-1030
MSC (2000): Primary 32H02, 32H35
Published electronically: November 17, 2005
MathSciNet review: 2196034
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ f$ be a rational proper holomorphic map between the unit ball in $ \mathbb{C}^2$ and the unit ball in $ \mathbb{C}^n.$ Write

$\displaystyle f=\dfrac{(p_1, \dots, p_n)}{q},$

where $ p_j, j=1, \dots,n,$ and $ q$ are holomorphic polynomials, with $ (p_1,\dots,p_{n},q)$ $ =1.$ Recall that the degree of $ f$ is defined by

   deg$\displaystyle f =$$\displaystyle \text {max}\{\text{deg} (p_j)_{j=1,\dots,n}, \text{deg} q\}.$

In this paper, we give a bound estimate for the degree of $ f,$ improving the bound given by Forstneric (1989).


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Additional Information

Francine Meylan
Affiliation: Institut de Mathématiques, Université de Fribourg, 1700 Perolles, Fribourg, Switzerland
Email: francine.meylan@unifr.ch

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08476-5
PII: S 0002-9939(05)08476-5
Received by editor(s): July 20, 2004
Published electronically: November 17, 2005
Additional Notes: The author was partially supported by Swiss NSF Grant 2100-063464.00/1
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2005 American Mathematical Society