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On gonality and canonical models of unicuspidal rational curves

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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.

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Acknowledgements

We thank the referee for many suggestions and corrections we built into this version. This work is part of the first named author’s Ph.D thesis. The second named author is partially supported by FAPEMIG RED-00133-21. We thank C. Carvalho, E. Cotterill, A. Fenandez and M. E. Hernandes for many suggestions as well.

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Authors and Affiliations

  1. Departamento de Matemática, ICEx, UFMG, Av. Antônio Carlos 6627, 30123-970, Belo Horizonte, MG, Brazil

    Naamã Galdino & Danielle Nicolau

  2. Departamento de Matemática, UFV / CAF, Rodovia LMG 818 km 06, 35690-000, Florestal, MG, Brazil

    Renato Vidal Martins

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  1. Naamã Galdino
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  2. Renato Vidal Martins
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Correspondence to Renato Vidal Martins.

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Communicated by Nathan Kaplan.

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Galdino, N., Martins, R.V. & Nicolau, D. On gonality and canonical models of unicuspidal rational curves. Semigroup Forum 107, 79–108 (2023). https://doi.org/10.1007/s00233-023-10354-1

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