Holomorphic mappings between spaces of different dimensions. II
type: Item
instance of: scholarly article
title: Holomorphic mappings between spaces of different dimensions. II
zbMATH Open document ID: 0791.58015
DOI: 10.1007/BF02571708
author: Pei-Chu Hu
published in: Mathematische Zeitschrift
publication date: 1994-05-10T00:00:00Z
full work available at URL: https://eudml.org/doc/174606
review text: In this part II of the paper [part I: the author, ibid. 214, No. 4, 567- 577 (1993; see the paper above)], the author proves the following result: Let \(f: \mathbb{C} \to N\) be a holomorphic mapping into a pseudo canonical complex projective variety \(N\). Then either \(f\) is algebraically degenerate or the image of \(f\) is autoparallel with respect to a meromorphic connection on \(N\). By using the result, we can prove a classical conjecture as follows: Let \(f: \mathbb{C} \to W\subset \mathbb{P}^ n\) be a holomorphic map to a hypersurface of degree at least \(n+2\). Then \(f\) is algebraically degenerate.
Mathematics Subject Classification ID: 58C10
zbMATH DE Number: 567396
zbMATH Keywords: spaces of different dimensions
zbMATH Keywords: holomorphic mapping
zbMATH Keywords: algebraically degenerate
MaRDI profile type: Publication
cites work: Compact Manifolds and Hyperbolicity
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cites work: Hyperbolic surfaces in \({\mathbb{P}}^ 3\)
cites work: Defect relations for holomorphic maps between spaces of different dimensions
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description: scientific article; zbMATH DE number 567396