2022•arXiv (Cornell University)Open access

Remarks on double points of plane curves

Alessandro Gimigliano, Monica Idà

Abstract

We study the relation between the type of a double point of a plane curve and the curvilinear 0-dimensional subschemes of the curve at the point. An Algorithm related to a classical procedure for the study of double points via osculating curves is described and proved. Eventually we look for a way to create examples of rational plane curves with given singularities $A_s$.

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Key concepts: Osculating circle, Plane curve, Mathematics, Plane (geometry), Curvilinear coordinates, Gravitational singularity, Quartic plane curve, Point (geometry)