The normal form of germs of four-dimensional real submanifolds in \(\mathbb{C}^5\) at generic \(\mathbb{R}\mathbb{C}\)-singular points
type: Item
instance of: scholarly article
title: The normal form of germs of four-dimensional real submanifolds in \(\mathbb{C}^5\) at generic \(\mathbb{R}\mathbb{C}\)-singular points
zbMATH Open document ID: 0917.32015
DOI: 10.1007/BF02361220
author: Valeriĭ K. Beloshapka
published in: Mathematical Notes
publication date: 1999-08-02T00:00:00Z
review text: The interest of \(RC\)-singular points of a closed real smooth oriented \(m\)-dimensional submanifold \(M\) of \(\mathbb{C}^n\) increases after the papers of H. T. Lai, A. V. Dornrin, J. K. Moser and S. M. Vebster (see the references of the paper). In fact, the problem is to characterize the germ of a surface at an \(RC\)-singular point. With the help of the normal form of the equation of the surface, Moser and Vebster discovered a rich system of holomorphic nonequivalent invariants of such germs in the case \(m=n=2\). Surprisingly, there are no biholomorphic invariants in the case \(n=5\), \(m=4\), and the equation of any generic germ at an \(RC\)-singular point can be reduced to a unique normal form. This is the main result of the author in this paper.
Mathematics Subject Classification ID: 32V40
Mathematics Subject Classification ID: 32C05
Mathematics Subject Classification ID: 32S25
zbMATH DE Number: 1238034
zbMATH Keywords: real submanifold
zbMATH Keywords: generic RC-singular point
zbMATH Keywords: holomorphic invariant
zbMATH Keywords: normal form
reviewed by: Stancho Dimiev
MaRDI profile type: Publication
cites work: Normal forms for real surfaces in \(C^ 2\) near tangents and hyperbolic surface transformations
full work available at URL: https://doi.org/10.1007/bf02361220
OpenAlex ID: W1966198100
description: scientific article; zbMATH DE number 1238034