On the polar quotients of an analytic plane curve
type: Item
instance of: scholarly article
title: On the polar quotients of an analytic plane curve
zbMATH Open document ID: 1007.32018
author: Janusz Gwoździewicz
author: Arkadiusz Płoski
published in: Kodai Mathematical Journal
publication date: 2002-08-18T00:00:00Z
review text: Let \(f \in \mathbb{C}\{x,y\}\) be a reduced power series and \(t\) a power series of order 1 not dividing \(f\). The polar quotients of \(f\) with respect to \(t\) are defined by \[ Q(f,t) = \left\{\frac{(f,\varphi)_0}{(t,\varphi)_0} \Bigg|\varphi \text{ an irreducible factor of } \frac{\partial(t,f)}{\partial(x,y)}\right\}, \] here \((f,\varphi)_0\) is the intersection multiplicity of \(f\) and \(\varphi\) at 0. An explicit formula in terms of characteristic exponents and intersection multiplicities of the branches for the polar quotients is given.
reviewed by: Gerhard Pfister
Mathematics Subject Classification ID: 32S10
Mathematics Subject Classification ID: 14H20
zbMATH DE Number: 1782966
zbMATH Keywords: plane curve singularity
zbMATH Keywords: polar quotients
zbMATH Keywords: Puiseux data
MaRDI profile type: Publication
OpenAlex ID: W2026352205
DOI: 10.2996/KMJ/1106171074
description: scientific article; zbMATH DE number 1782966