On Gonality and Canonical Models of Unicuspidal Rational Curves

We study the gonality and canonical model of a rational unicuspidal curve C. We are mainly interested in the case where C is non-Gorenstein. We classify such curves via different notions of gonality, and by its canonical model C', up to genus 6. We do it by means of more general families of curves of arbitrary genus. Afterwards, we get a general formula for the dimension of the space of hypersurfaces of a fixed degree containing C', which we apply to some particular cases.