An application of the lemma on the logarithmic derivative in several complex variables due to A. Vitter
type: Item
instance of: scholarly article
title: An application of the lemma on the logarithmic derivative in several complex variables due to A. Vitter
zbMATH Open document ID: 0582.32031
author: Seiki Mori
published in: Kodai Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: Another proof of the following particular case of a theorem of \textit{K. Kodaira} [J. Differ. Geom. 6, 33-46 (1971; Zbl 0227.32008)] is stated: A holomorphic map of \({\mathbb{C}}^ n\) into a smooth hypersurface of degree greater than \(n+2\) in \({\mathbb{P}}^{n+1}\) must be degenerate. The present proof uses \textit{A. Vitter}'s form of Nevanlinna's lemma on logarithmic derivatives [Duke Math. J. 44, 89-104 (1977; Zbl 0361.32003)].
reviewed by: Fumio Sakai
Mathematics Subject Classification ID: 32H25
zbMATH DE Number: 3931401
zbMATH Keywords: holomorphic map
zbMATH Keywords: hypersurface
zbMATH Keywords: degenerate
zbMATH Keywords: Nevanlinna's lemma on logarithmic derivatives
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138036855
OpenAlex ID: W1983799187
Wikidata QID: Q124829675
cites work: A defect relation for equidimensional holomorphic mappings between algebraic varieties
cites work: Q4753437
cites work: Some Picard Theorems for Holomorphic Maps to Algebraic Varieties
cites work: Q5723337
cites work: Holomorphic mappings of polydiscs into compact complex manifolds
cites work: The lemma of the logarithmic derivative in several complex variables
DOI: 10.2996/KMJ/1138036855
description: scientific article; zbMATH DE number 3931401