Abschätzungen für die Anzahl der holomorphen Abbildungen zwischen algebraischen Räumen. (Estimates for the number of holomorphic mappings between algebraic varieties)
type: Item
instance of: scholarly article
title: Abschätzungen für die Anzahl der holomorphen Abbildungen zwischen algebraischen Räumen. (Estimates for the number of holomorphic mappings between algebraic varieties)
zbMATH Open document ID: 0594.32026
DOI: 10.1007/BF01215141
author: Klaus Langmann
published in: Mathematische Zeitschrift
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/173636
review text: Let X be ''algebraic'' in the following sense: X is a projective algebraic variety minus a subvariety. An upper bound is given for the number of nonconstant holomorphic functions which omit q distinct values \(\{b_ 1=0\), \(b_ 2=1\), \(b_ 3,...,b_ q\}\). A number of results are given which bound the number of mappings from X to an algebraic Y. For instance, if there is a finite holomorphic mapping from Y to a finite product of copies of \({\mathbb{C}}\setminus \{0,1\},\) then there are only finitely many nondegenerate mappings \(f: X\to Y\).
Mathematics Subject Classification ID: 32H25
Mathematics Subject Classification ID: 14E99
zbMATH DE Number: 3955405
zbMATH Keywords: Picard exponent
zbMATH Keywords: Picard theorem
zbMATH Keywords: omitted value
zbMATH Keywords: holomorphic mapping
MaRDI profile type: Publication
cites work: Some Picard Theorems for Holomorphic Maps to Algebraic Varieties
cites work: Anwendungen des Satzes von Picard
description: scientific article; zbMATH DE number 3955405