On proper holomorphic mappings between rigid polynomial domains in \(\mathbb C^{n+1}\)
type: Item
instance of: scholarly article
title: On proper holomorphic mappings between rigid polynomial domains in \(\mathbb C^{n+1}\)
zbMATH Open document ID: 1073.32008
author: Nabil Ourimi
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: A rigid polynomial domain in \(\mathbb{C}^{n+1}\) is one which is given as \[ \{(z_0, z)\in \mathbb{C}^{n+1}: r(z_0, z)= 2\text{\,Re}(z_0)+ P(z,\overline z)< 0\}, \] where \(P(z,\overline z)\) is a polynomial. In this paper the author proves the following theorem: Let \(D\) and \(D'\) be rigid polynomial nondegenerate domains in \(\mathbb{C}^{n+1}\). Then the branch locus of any proper holomorphic mapping \(f: D\to D'\) (denoted by \(V_f)\) satisfies \[ V_f\subset \bigcup_{1\leq k\leq N} \{(z_0, z)\in D: z\in\widehat B_k\}. \]
Mathematics Subject Classification ID: 32H35
Mathematics Subject Classification ID: 32D10
zbMATH DE Number: 2141740
zbMATH Keywords: Proper holomorphic mappings
zbMATH Keywords: Rigid polynomial nondegenerate domains
zbMATH Keywords: Segre varieties
zbMATH Keywords: Envelope of holomorphy
reviewed by: Miloš Čanak
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.06.010
OpenAlex ID: W1977396606
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cites work: Q3993490
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DOI: 10.1016/J.JMAA.2004.06.010
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description: scientific article; zbMATH DE number 2141740