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The gonality sequence of covering curves

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Abstract

According to Kato and Martens (Arch Math 103:111–116, 2014), the gonality sequence of a curve X of genus g which doubly covers a curve Y of genus h > 0 is completely determined by the gonality sequence of the covered curve Y provided that g is sufficiently large w.r.t. h. In this paper we study how far this result can be extended to a covering X/Y of degree m > 2. It turns out that it is useful for this question to introduce the notion of irrational gonality of X, and we will show that for prime m or if m is the irrational gonality of X several results valid for m = 2 remain true. The best results are obtained for m = 3; in particular, the case of “tri-elliptic” X (i.e. m = 3, h = 1) is extensively worked out.

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Authors and Affiliations

  1. Department of Mathematics, Seoul National University, Seoul, 151-742, South Korea

    Changho Keem

  2. Department Mathematik, University of Erlangen-Nürnberg, Cauerstr. 11, 91058, Erlangen, Germany

    Gerriet Martens

Authors
  1. Changho Keem
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  2. Gerriet Martens
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Corresponding author

Correspondence to Gerriet Martens.

Additional information

The first named author was supported in part by the grant NRF 2011-0010298. The second author wants to thank Takao Kato for his useful suggestions.

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Keem, C., Martens, G. The gonality sequence of covering curves. Arch. Math. 105, 33–43 (2015). https://doi.org/10.1007/s00013-015-0758-1

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  • DOI: https://doi.org/10.1007/s00013-015-0758-1

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