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Gonality of non-Gorenstein curves of genus five

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Abstract

We establish sufficient conditions for some curves to be trigonal and derive from them that most of non-Gorenstein curves of genus five are so. Afterwards, we show that the gonality of such a curve ranges from 2 to 5. Gonality is understood within a broader context, i.e., the g 1 d may possibly admit a base point and correspond to a torsion free sheaf of rank one instead of a line bundle. This study comes along with a thorough description of possible canonical models and kinds of singularities.

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Authors and Affiliations

  1. Departamento de Matemática, CCE, UFV, Av. P H Rolfs s/n, 36570-000, Viçosa, MG, Brazil

    Lia Feital

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

    Renato Vidal Martins

Authors
  1. Lia Feital
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  2. Renato Vidal Martins
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Correspondence to Renato Vidal Martins.

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Dedicated to Steven Lawrence Kleiman, for his 70th birthday.

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Feital, L., Martins, R.V. Gonality of non-Gorenstein curves of genus five. Bull Braz Math Soc, New Series 45, 649–670 (2014). https://doi.org/10.1007/s00574-014-0067-5

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  • DOI: https://doi.org/10.1007/s00574-014-0067-5

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