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Zbl 0749.32016
Gruman, Lawrence
The image of a holomorphic mapping. (L'image d'une application holomorphe.) (French)
[J] Ann. Fac. Sci. Toulouse, V. Sér., Math. 12, No.1, 75-101 (1991). ISSN 0240-2955

The author first describes a method of constructing the discrete essential sets in $\bbfC\sp n$ such that for every nondegenerate holomorphic mapping $F:\bbfC\sp n\to\bbfC\sp n$ the image of $\bbfC\sp n$ under $F$ intersects these sets, then in the same way constructs a family $E\sb a$ of such discrete sets parametrized by a point $a\in\bbfC\sp n$ possessing the following property: Let $B(0,r)$ be an open Euclidean ball of the center 0 and radius $r$, the asymptotic growth of domains $F\sp{- 1}(E\sb a)\cap B(0,r)$ as $r\to\infty$ is the same, except perhaps for an exceptional set of $a$ which is pluripolar in $\bbfC\sp n$, and this asymptotic growth can be expressed as a function of $\log M(r)=\sup\sb{z\in B(0,r)}\log\Vert F(z)\Vert$.
[Na Jisheng (Beijing)]

MSC 2000:: *32H02 Holomorphic mappings on analytic spaces
32H30 Value distribution theory in higher dimensions

Keywords: holomorphic mapping; image of nondegenerate holomorphic mapping; asymptotic growth

Cited in: Zbl 0929.32003 Zbl 0910.32028

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