Newton-Puiseux algorithm and triple points for planes curves

Stefano Canino; Alessandro Gimigliano; Monica Idà

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arXiv · 2204.05691

Newton-Puiseux algorithm and triple points for planes curves

Stefano Canino·Alessandro Gimigliano·Monica Idà

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Abstract

The paper is an introduction to the use of the classical Newton-Puiseux procedure, oriented to an algorithmic description of it. This procedure enables to get polynomial approximations for parameterizations of branches of an algebraic plane curve at a singular point. We look for an approach that can be easily grasped and almost self contained. We illustrate the use of the algorithm, first in a completely worked out example of a curve with a point of multiplicity 6, and secondly in the study of triple points on reduced plane curves.

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Stefano Canino, Alessandro Gimigliano, Monica Idà. 2022-04-12. Newton-Puiseux algorithm and triple points for planes curves. https://arxiv.org/abs/2204.05691

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