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Numerical semigroups of genus six and double coverings of curves of genus three

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Abstract

This is a sequel of previous papers of the authors on Weierstrass semigroups at ramification points of double coverings of algebraic curves of genus three. In this paper they give a list of possible numerical semigroups when the covering curve is of genus six and show that all of such semigroups are actually of double covering type. This result completes a classification of numerical semigroups of double covering type obtained by ramified double coverings of curves of genus three.

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Authors and Affiliations

  1. Department of Core Studies, Kochi University of Technology, Kami, Tosayamada, Kochi, 782-8502, Japan

    Takeshi Harui

  2. Department of Mathematics, Center for Basic Education and Integrated Learning, Kanagawa Institute of Technology, Atsugi, Kanagawa, 243-0292, Japan

    Jiryo Komeda

Authors
  1. Takeshi Harui
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  2. Jiryo Komeda
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Correspondence to Takeshi Harui.

Additional information

Communicated by Fernando Torres.

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Harui, T., Komeda, J. Numerical semigroups of genus six and double coverings of curves of genus three. Semigroup Forum 91, 601–610 (2015). https://doi.org/10.1007/s00233-014-9671-3

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  • DOI: https://doi.org/10.1007/s00233-014-9671-3

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