An extension of the derivative of meromorphic functions to holomorphic curves
type: Item
instance of: scholarly article
title: An extension of the derivative of meromorphic functions to holomorphic curves
zbMATH Open document ID: 0810.30020
author: Nobushige Toda
published in: Proceedings of the Japan Academy. Series A
publication date: 1994-12-19T00:00:00Z
review text: Let \(f: \mathbb{C}\to P^ n(\mathbb{C})\) be a holomorphic curve and \[ (f_ 1,f_ 2,\dots, f_{n_ 1}): \mathbb{C}\to \mathbb{C}^{n+1}\backslash \{0\} \] be a reduced representation of \(f\). The author introduces a sort of derivative to holomorphic curves as follows: Let \(W(f_ 1,f_ 2,\dots, f_{n+1})\) be the Wronskian of \(f_ 1,f_ 2,\dots, f_{n+1}\), then the derived holomorphic curve of \(f\), denoted by \(f^*\), is the mapping \[ (f^{n+1}_ 1,\dots, f^{n+1}_ n,\;W(f_ 1,\dots, f_{n+1})): \mathbb{C}\to \mathbb{C}^{n+1}. \] The author proves that \(f^*\) possesses some similar properties to the derivative of meromorphic functions.
reviewed by: Yuzan He
Mathematics Subject Classification ID: 30D35
Mathematics Subject Classification ID: 30D30
zbMATH DE Number: 701473
zbMATH Keywords: derivative
zbMATH Keywords: holomorphic curve
MaRDI profile type: Publication
full work available at URL: pjaa.70.159
OpenAlex ID: W2012452057
cites work: Q4753437
cites work: Q5723337
cites work: Sum of deficiencies and the order of a meromorphic function
cites work: Holomorphic curves with maximal deficiency sum
cites work: Sur une relation entre la croissance et le nombre de valeurs déficientes de fonctions algébroï des ou de systèmes
cites work: On the order of holomorphic curves with maximal deficiency sum
DOI: 10.3792/PJAA.70.159
description: scientific article; zbMATH DE number 701473