Geometric deformations of implicit curves
Differential Geometry
2025-02-28 v1
Abstract
Let f = 0 be an implicit singular plane curve. When deforming f = 0, inflections and vertex emerge from the singularities. In this papper, we classify the deformations of f = 0 with respect to the inflections and the vertices in the cases of codimension less than or equal to 2, that is, in the cases that occur generically in families of implicit curves with 2 parameters.
Keywords
Cite
@article{arxiv.2502.19509,
title = {Geometric deformations of implicit curves},
author = {Marco Antônio do Couto Fernandes and Samuel Paulino dos Santos},
journal= {arXiv preprint arXiv:2502.19509},
year = {2025}
}