Discriminant of a germ \((g,f): (\mathbb{C}^2,0)\to (\mathbb{C}^2,0)\) and contact quotients in the resolution of \(f\cdot g\)
type: Item
instance of: scholarly article
title: Discriminant of a germ \((g,f): (\mathbb{C}^2,0)\to (\mathbb{C}^2,0)\) and contact quotients in the resolution of \(f\cdot g\)
zbMATH Open document ID: 0936.32012
author: Hélène Maugendre
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1999-05-26T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73463
review text: Let \(f: \mathbb C^2\to\mathbb C\) and \(g: \mathbb C^2\to\mathbb C\) be two germs of plane curves. The Jacobian of the map \((g,f)\) defines the Jacobian curve whose image is the discriminant. The first Puiseux pairs of all branch give a set of rational numbers, which are called Jacobian quotients. In the case where \(g\) is a transverse linear form one obtains the polar quotients. The author describes how to compute these quotients in terms of a simultaneous embedded resolution of \(f\) and \(g\). As application the case that the reduced Jacobian curve is smooth is studied.
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 32S45
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 14B05
zbMATH DE Number: 1279201
zbMATH Keywords: Jacobian quotients
zbMATH Keywords: polar quotients
reviewed by: Jan Stevens
MaRDI profile type: Publication
OpenAlex ID: W2313887638
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DOI: 10.5802/AFST.908
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description: scientific article; zbMATH DE number 1279201