Polar curves
type: Item
instance of: scholarly article
title: Polar curves
zbMATH Open document ID: 0872.14040
author: Abramo Hefez
author: Neuza Kakuta
published in: Journal of Algebra
publication date: 1996-07-09T00:00:00Z
full work available at URL: http://hdl.handle.net/11449/32426
review text: Let \(C\) be a plane curve of degree \(d\). For every integer \(t>0\) and every \(Q\in \mathbb{P}^2\) it is defined the polar curve of \(C\) of order \(t\) with respect to \(Q\). The characteristic 0 case was classical. Here the authors extend the general definitions to the positive characteristic case using Hasse derivations. They make a very detailed analysis of the pathologies arising in characteristic \(p\), giving very nice classifications of the examples with ``extremal'' behaviour and the analysis (in terms of \(d\), \(t\) and \(p)\) of the case of a general \(C\) and of a curve \(C\) with ``mild'' singularities. Then they introduce the polar morphisms of plane curves, which generalize the Gauss map, and prove a formula that generalizes Plücker's formula relating the degree of a curve, the degree of its Gauss map, and the degree of its dual curve.
reviewed by: E. Ballico
Mathematics Subject Classification ID: 14N05
Mathematics Subject Classification ID: 14G20
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 883769
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: Frobenius map
zbMATH Keywords: plane curve
zbMATH Keywords: polar curve
zbMATH Keywords: Hasse derivations
zbMATH Keywords: polar morphisms
zbMATH Keywords: Gauss map
zbMATH Keywords: Plücker's formula
MaRDI profile type: Publication
OpenAlex ID: W3023020124
DOI: 10.1006/JABR.1996.0129
Recommended article: Q2703213
Recommended article: Polar curves in the non-Euclidean geometry
Recommended article: Q4946726
Recommended article: Base points of polar curves
Recommended article: Single-valued curves in polar coordinates
description: scientific article; zbMATH DE number 883769