Singular foliations of toric type
type: Item
instance of: scholarly article
title: Singular foliations of toric type
zbMATH Open document ID: 0964.32029
author: Felipe Cano
author: Maria Izabel Tavares Camacho
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 2001-07-08T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73480
review text: A germ \(\mathcal F\) of a singular foliation at \(0\in{\mathbb C}^2\) is said to be of toric type if there is a toric modification of \({\mathbb C}^2\) that desingularizes \(\mathcal F\). The authors offer an algorithm that achieves this, if it is possible at all, in an explicit way, by choosing coordinates in \({\mathbb C}^2\) suitably. To do this, they choose a normal crossings divisor \(D\) which is invariant under \(\mathcal F\), and write the form \(\omega\) that determines \(\mathcal F\) in terms of local coordinates in which \(D\subseteq \{xy=0\}\). This determines a Newton polygon, and the coordinates are then to be modified so as to simplify the polygon.
Mathematics Subject Classification ID: 32S65
Mathematics Subject Classification ID: 14M25
zbMATH DE Number: 1491213
zbMATH Keywords: singular foliations of toric type
zbMATH Keywords: Newton polygon
reviewed by: G. K. Sankaran
MaRDI profile type: Publication
OpenAlex ID: W2322233404
cites work: Q4039830
DOI: 10.5802/AFST.921
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description: scientific article; zbMATH DE number 1491213