Domains of holomorphy in Segre cones
type: Item
instance of: scholarly article
title: Domains of holomorphy in Segre cones
zbMATH Open document ID: 0617.32016
author: Tetsuo Ueda
published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University
publication date: 1986-01-01T00:00:00Z
review text: Consider the space \({\mathbb{C}}^{rs}\) as the set of all rs-matrices with complex components. Let D be a domain in the Segre cone \(Z=\{z\in {\mathbb{C}}^{rs}:\) rank \(z\leq 1\}\). The author's main result says that if D is locally Stein at every non-singular boundary point in \(Z\setminus \{0\}\), then either D is a domain of holomorphy or the origin is an isolated boundary point of D, D is not a domain of holomorphy and \(D\cup \{0\}\) is a Stein domain. The method of the proof is similar to that in a previous author's paper [J. Math. Kyoto Univ. 20, 391-394 (1980; Zbl 0456.32011)], namely to go over a vector space and to apply Oka's theorem. As a consequence, D is Stein if it is locally Stein at every boundary point.
reviewed by: Johann Davidov
Mathematics Subject Classification ID: 32D05
Mathematics Subject Classification ID: 32E10
Mathematics Subject Classification ID: 32T99
zbMATH DE Number: 4000357
zbMATH Keywords: Segre cone
zbMATH Keywords: domain of holomorphy
zbMATH Keywords: Stein domain
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2977/prims/1195177853
OpenAlex ID: W2087531171
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DOI: 10.2977/PRIMS/1195177853
description: scientific article; zbMATH DE number 4000357