A unicity theorem for meromorphic maps of a complete Kähler manifold into \({\mathbb{P}}^ N({\mathbb{C}})\)
type: Item
instance of: scholarly article
title: A unicity theorem for meromorphic maps of a complete Kähler manifold into \({\mathbb{P}}^ N({\mathbb{C}})\)
zbMATH Open document ID: 0599.32001
author: Hirotaka Fujimoto
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1986-01-01T00:00:00Z
review text: Généralisant le théorème d'unicité de \textit{R. Nevanlinna} [Acta Math. 48, 367-391 (1926)] pour les fonctions méromorphes sur \({\mathbb{C}}\), on détermine un entier q tel que deux applications méromorphes non dégénérées f,g: \({\mathbb{C}}^ n\to P^ N({\mathbb{C}})\) soient identiques si elles coïncident sur la réunion des \(f^{-1}(H_ j)\) et \(g^{-1}(H_ j)\), où les \(H_ j\) sont q hyperplans de \({\mathbb{C}}^ n\) en position générale. On remplace ensuite \({\mathbb{C}}^ n\) par une variété kählerienne complète et connexe dont le revêtement universel est analytiquement isomorphe à \({\mathbb{C}}^ n\) ou une boule de \({\mathbb{C}}^ n:\) la valeur de q fait alors intervenir la forme de Ricci de la métrique kählerienne.
Mathematics Subject Classification ID: 32A20
Mathematics Subject Classification ID: 32A30
Mathematics Subject Classification ID: 53C55
Mathematics Subject Classification ID: 30D30
zbMATH DE Number: 3966661
zbMATH Keywords: unicity theorem of Nevanlinna
zbMATH Keywords: meromorphic maps
zbMATH Keywords: Kähler manifold
reviewed by: Rose-Marie Hervé
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228497
OpenAlex ID: W2164171270
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DOI: 10.2748/TMJ/1178228497
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description: scientific article; zbMATH DE number 3966661