On the number of cusps on cuspidal curves on Hirzebruch surfaces

TL;DR

This paper establishes an upper bound on the number of cusps on cuspidal curves on Hirzebruch surfaces, adapting known results from the projective plane to this new geometric setting.

Contribution

It extends existing bounds for cuspidal curves from the projective plane to Hirzebruch surfaces, providing new insights in algebraic geometry.

Findings

Derived an explicit upper bound for cusps on curves on Hirzebruch surfaces

Adapted methods from projective plane to Hirzebruch surface setting

Restated classical results in a broader geometric context

Abstract

In this article we give an upper bound for the number of cusps on a cuspidal curve on a Hirzebruch surface. We adapt the results that have been found for a similar question asked for cuspidal curves on the projective plane, and restate the results in this new setting.