Transcendental submanifolds of projective space
type: Item
instance of: scholarly article
title: Transcendental submanifolds of projective space
zbMATH Open document ID: 1209.57023
DOI: 10.4171/CMH/154
published in: Commentarii Mathematici Helvetici
publication date: 2009-02-16T00:00:00Z
full work available at URL: http://www.ems-ph.org/journals/show_pdf.php
review text: Summary: Given integers \(m\) and \(c\) satisfying \(m - 2 \geq c \geq 2\), we explicitly construct a nonsingular \(m\)-dimensional algebraic subset of \(\mathbb P^{m + c}(\mathbb R)\) that is not isotopic to the set of real points of any nonsingular complex algebraic subset of \(\mathbb P^{m + c}(\mathbb C)\) defined over \(\mathbb R\). The first examples of this type were obtained by Akbulut and King in a more complicated and nonconstructive way, and only for certain large integers \(m\) and \(c\).
Mathematics Subject Classification ID: 57R55
Mathematics Subject Classification ID: 14P25
zbMATH DE Number: 5508255
zbMATH Keywords: smooth manifold
zbMATH Keywords: algebraic set
zbMATH Keywords: isotopy
author: Wojciech Kucharz
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5508255