On gonality and canonical models of unicuspidal rational curves

We study the gonality of a curve C and its canonical model C ′ , by means of unicuspidal rational curves, where those concepts can be better understood. We start by a general formula for the dimension of the space of hypersurfaces of a fixed degree containing C ′ , which we apply to some particular cases. Then we classify unicuspidal rational curves via different notions of gonality, and by its canonical model, up to genus 6. We do it using general methods applied to certain families of curves of arbitrary genus.