Some Geometry of Nodal Curves

TL;DR

This paper introduces a geometric approach to analyze singularities of plane nodal curves, which are fundamental in algebraic geometry due to their relation to all projective curves.

Contribution

It presents a novel geometric method for studying singularities of plane nodal curves, with applications to Plucker formulas and curve classification.

Findings

Developed a new geometric analysis technique for nodal curve singularities

Established foundational results for future work on Plucker formulas

Enhanced understanding of the structure of plane nodal curves

Abstract

We find a geometrical method of analysing the singularities of a plane nodal curve. The main results will be used in a forthcoming paper on geometric Plucker formulas for such curves. Plane nodal curves, that is plane curves having at most nodes as singularities, form an important class of curves, as any projective algebraic curve is birational to a plane nodal curve.