On the classification of foliations of degree three with one singularity
type: Item
instance of: scholarly article
title: On the classification of foliations of degree three with one singularity
zbMATH Open document ID: 1495.32057
author: S. C. Coutinho
published in: Journal of Symbolic Computation
publication date: 2022-03-21T00:00:00Z
review text: A degree-\(d\) foliation on \(\mathbb{P}^2\) can be defined by a homogeneous vector field \(v\) of degree \(d\), not vanishing in codimension one. It is known that \(v\) must vanish at \(d^2 + d+ 1\) points, called singularities, counted with multiplicities; for a generic \(v\) they are all distinct. Foliations with only one singularity (of multiplicity \(d^2 + d+ 1\)) are rather special and their classification is an interesting problem, of which the article under review solves a particular case. Precisely, the author proves that any foliation of degree \(d=3\) with nontrivial finite isotropy group and only one singularity must fit, up to change of coordinates, in one of 7 families of foliations \(\mathcal{F}_j\), \(1\leq j \leq 7\) described in the paper. The proof is based on an algorithm written for AXIOM.
reviewed by: Alan Muniz
Mathematics Subject Classification ID: 32M25
Mathematics Subject Classification ID: 32S65
zbMATH DE Number: 7493809
zbMATH Keywords: singularity
zbMATH Keywords: holomorphic foliation
zbMATH Keywords: algebraic solution
describes a project that uses: AXIOM
describes a project that uses: SINGULAR
MaRDI profile type: Publication
full work available at URL: j.jsc.2022.01.001
OpenAlex ID: W4205457124
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DOI: 10.1016/J.JSC.2022.01.001
description: scientific article; zbMATH DE number 7493809