Remark on Tono's theorem about cuspidal curves

TL;DR

This paper establishes an upper bound on the number of cusps of plane curves based on their first Betti number, providing a new geometric constraint.

Contribution

It introduces a novel upper bound for cusps in plane curves using topological invariants, extending Tono's theorem.

Findings

Upper bound on cusps in terms of first Betti number

Application to affine and projective curves

Enhanced understanding of curve singularities

Abstract

We give an upper bound for the number of cusps of a plane affine or projective curve via its first Betti number.