On vertices and inflections of plane curves

Fabio Scalco Dias and Farid Tari

Journal of Singularities
volume 17 (2018), 70-80

Received: 9 November 2017. Received in revised form: 19 February 2018

DOI: 10.5427/jsing.2018.17d

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Abstract:

We count the number of inflections (I) and vertices (V) concentrated at the singularity of a germ of a parametrised plane curve and show that V=I+\mu-2, where \mu is the Milnor number of a certain singularity.

Keywords:

bifurcations, evolutes, plane curves, inflections, vertices, singularities

2010 Mathematical Subject Classification:

53A04, 58K05, 58K60

Author(s) information:

Fabio Scalco Dias	Farid Tari
Instituto de Matemática e Computação	Instituto de Ciências Matemáticas
Universidade Federal de Itajubá	e de Computação
Avenida BPS 1303, Pinheirinho	Universidade de São Paulo
CEP 37.500-903, Itajubá, MG, Brazil	Avenida Trabalhador são-carlense
	400 - Centro
	CEP: 13566-590 - São Carlos - SP, Brazil
email: scalco@unifei.edu.br	email: faridtari@icmc.usp.br