Low degree points on singular plane curves

TL;DR

This paper investigates low degree points on singular plane curves, establishing results similar to prior work for curves with a limited number of nodes and cusps, bounded quadratically by the degree.

Contribution

It extends existing theories to singular plane curves with bounded singularities, providing new bounds and analogues of classical results.

Findings

Results analogous to Debarre and Klassen for singular curves

Bound on the number of singularities quadratic in degree

New bounds for low degree points on singular plane curves

Abstract

The purpose of this paper is to study low degree points on plane curves. We prove results analogous to those of Debarre and Klassen for singular plane curves with a finite number $\delta$ of ordinary nodes/cusps, where $\delta$ is bounded from above by a quadratic function in the degree of the plane curve.