Linear webs and algebraization theorems of inverse-Abel and inverse-Reiss type
type: Item
instance of: scholarly article
title: Linear webs and algebraization theorems of inverse-Abel and inverse-Reiss type
zbMATH Open document ID: 0868.53015
DOI: 10.1023/A:1004916502107
author: Alain Hénaut
published in: Geometriae Dedicata
publication date: 1997-06-02T00:00:00Z
review text: A \(d\)-web \(W (d)\) of codimension one in \((\mathbb{C}^n, 0)\) is given by \(d\) complex analytic foliations of codimension one of \((\mathbb{C}^n, 0)\) which are in general position. A web \(W (d)\) is called linear if the leaves of all its foliations are hyperplanes (or pieces of hyperplanes) in \((\mathbb{C}^n, 0)\). A linear web \(W (d)\) is called algebraic is it is associated by duality to a nondegenerate algebraic curve \(\Gamma\) of degree \(d\) of a projective space \(P^n\). The author characterizes linear webs \(W (d) \subset (\mathbb{C}^n, 0)\) by giving two necessary and sufficient conditions for \(W (d)\) to be linear. He also gives three explicit equivalent conditions under which a linear web \(W (d) \subset (\mathbb{C}^n, 0)\) is algebraic and obtains equations for \(\Gamma \subset P^n\) in this case.
Mathematics Subject Classification ID: 53A60
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 1003885
zbMATH Keywords: linear web
zbMATH Keywords: algebraic web
reviewed by: Vladislav V. Goldberg
MaRDI profile type: Publication
full work available at URL: a:1004916502107
OpenAlex ID: W140889873
description: scientific article; zbMATH DE number 1003885