On some hypersurfaces and holomorphic mappings
type: Item
instance of: scholarly article
title: On some hypersurfaces and holomorphic mappings
zbMATH Open document ID: 0942.32018
author: Manabu Shirosaki
published in: Kodai Mathematical Journal
publication date: 2000-08-10T00:00:00Z
review text: Let \(d\) and \(p\) be two positive integers with \(d>2p+8\), \(P_1 (w_0,w_1)=w^d_0+w^p_0 w^{d-p}_1+ w^d_1\) a homogeneous polynomial with degree \(d\), and inductively, \(P_n(w_0, \dots,w_n)=P_{n-1} (P_1(w_0,w_1), \dots, P_1 (w_{n-1}, w_n))\) with degree \(d^n\) for \(n>2\). The author proves a number of theorems about holomorphic mappings related to \(P_n\). For example, the author shows that if \(f\) is a holomorphic mapping from \(\mathbb{C}\) into \(\mathbb{P}^n\) with a reduced representation \((f_0,\dots,f_n)\) and if \(P_n(f_0, \dots, f_n)= \alpha^{d^n}\) for some entire function \(\alpha\), then \(f\) is constant.
reviewed by: Zhuan Ye
Mathematics Subject Classification ID: 32H25
zbMATH DE Number: 1208193
zbMATH Keywords: hypersurface
zbMATH Keywords: hyperbolicity
zbMATH Keywords: holomorphic mappings
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138043832
OpenAlex ID: W2001563687
cites work: Q3764425
cites work: On polynomials which determine holomorphic mappings
DOI: 10.2996/KMJ/1138043832
description: scientific article; zbMATH DE number 1208193