Defining equations of certain rational cuspidal curves. I
type: Item
instance of: scholarly article
title: Defining equations of certain rational cuspidal curves. I
zbMATH Open document ID: 0994.14019
author: Keita Tono
published in: Manuscripta Mathematica
publication date: 2002-10-03T00:00:00Z
review text: The curves which are studied in this paper are irreducible plane curves \(C\) (over the complex field) which possess only one singular point \(P\) which is a cusp (unicuspidal curve), and such that the line \(l\) which is the multiple tangent at \(P\) meets \(C\) only in \(P\) (curve of Abhyankar-Moh-Suzuki type, AMS type). The main result in the paper is a theorem which explains how to pass with Cremona transformation from a curve \(C\) of AMS type to a line through \(P\), gives the multiplicity sequence at \(P\) of every curve at each step and how the equations of the curves are related to each other. The main tools for the proof are a detailed study of the effect of elementary transformations on germs of curve and De Jonquières transformations.
reviewed by: Alessandro Gimigliano
Mathematics Subject Classification ID: 14H20
Mathematics Subject Classification ID: 14E07
Mathematics Subject Classification ID: 14H50
zbMATH DE Number: 1546893
zbMATH Keywords: plane curves
zbMATH Keywords: cusp
zbMATH Keywords: rational curve
zbMATH Keywords: unicuspidal curve
zbMATH Keywords: Cremona transformation
zbMATH Keywords: curve of AMS type
zbMATH Keywords: De Jonquières transformations
MaRDI profile type: Publication
full work available at URL: s002290070028
OpenAlex ID: W1974870205
DOI: 10.1007/S002290070028
description: scientific article; zbMATH DE number 1546893