Maps between \(B^n\) and \(B^N\) with geometric rank \(k_0\leq n-2\) and minimum \(N\)
type: Item
instance of: scholarly article
title: Maps between \(B^n\) and \(B^N\) with geometric rank \(k_0\leq n-2\) and minimum \(N\)
zbMATH Open document ID: 1078.32011
author: Shanyu Ji
author: De Kang Xu
published in: The Asian Journal of Mathematics
publication date: 2005-03-21T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ajm/1088090061
review text: Let \(\text{Rat}(B^n, B^N)\) the set of rational proper holomorphic maps of \(B^n\) into \(B^N\) \((2\leq n\leq N)\), \(B^N\) denoting the unit ball in \(\mathbb{C}^N\). Using the notion of geometric rank introduced by X. Huang in 2003, the authors prove: Theorem 1.1. Let \(F\in \text{Rat}(B^n, B^N)\) with geometric rank \(\kappa_0\), \(1\leq\kappa_0\leq n-2\), and with \(N= n+{(2n-\kappa_0- 1)\kappa_0\over 2}\). Then \(\deg(F)\leq \kappa_0+ 2\). Theorem 1.2. Let \(F\in \text{Rat}(B^4, B^9)\) with the geometric rank 2 and with \(\deg(F)= 2\). Then \(F\) is equivalent to Whitney map \(W_{4,2}\) of rank 2.
reviewed by: Thanh Van Nguyen
Mathematics Subject Classification ID: 32H35
zbMATH DE Number: 2148820
zbMATH Keywords: rational proper holomorphic maps
zbMATH Keywords: geometric rank
zbMATH Keywords: Whitney map
MaRDI profile type: Publication
OpenAlex ID: W1969488791
DOI: 10.4310/AJM.2004.V8.N2.A4
description: scientific article; zbMATH DE number 2148820