The goal of this work is the study of the gonality 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.

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