Holomorphic Mappings from ℂn to ℂm

Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 282)


We shall study four problems here related to entire mappings defined on ℂ n . If X is a Cousin data in ℂ n , we have seen in Chapter 3 that we can define X as the zero set of an entire function f whose growth is related to the growth of v x (r), the indicator of X. Our first task will be to show a similar property for analytic varieties Y of arbitrary co-dimension in ℂ n . We shall show that we can define Y as Y = {z: F(z) = 0} where F: ℂ n →ℂ n +1 and the growth of ǁFǁ is bounded by v y (r), the projective indicator of growth of the current of integration on the analytic set Y (cf. Definition 2.24).


Analytic Variety Holomorphic Mapping Entire Function Regular Point Finite Order 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  1. 1.Université Paris VIParis Cedex 05France
  2. 2.UER de mathématiquesC.N.R.S., Université de ProvenceMarseilleFrance

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