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Weierstrass jump sequences and gonality

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Abstract

We prove some structure results on Weierstrass points on a non-hyperelliptic curve, which are total or almost total ramification points for the gonal covering. It turns out that the corresponding Weierstrass semigroup is strictly related to the splitting type of the gonal scroll containing the canonical model of the curve. We also give a description of the Weierstrass gap sequence in the case of a non ramification point for the gonal cover.

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Acknowledgments

The authors are grateful for the referees’ comments, which were very useful in clarifying the paper. The first author is supported by MIUR funds, PRIN Project Geometria delle varietà algebriche (2010), coordinator A. Verra, and by funds of the Università degli Studi di Trieste-Finanziamento di Ateneo per progetti di ricerca scientifica-FRA 2013. The first author is also supported by GNSAGA of INdAM.

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Authors and Affiliations

  1. Dipartimento di Matematica e Geoscienze, Università di Trieste, via Valerio 12/b, 34127, Trieste, Italy

    Valentina Beorchia

  2. Località S. Croce 159, 34151, Trieste, Italy

    Gianni Sacchiero

Authors
  1. Valentina Beorchia
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  2. Gianni Sacchiero
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Corresponding author

Correspondence to Valentina Beorchia.

Additional information

Communicated by Fernando Torres.

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Beorchia, V., Sacchiero, G. Weierstrass jump sequences and gonality. Semigroup Forum 92, 598–632 (2016). https://doi.org/10.1007/s00233-015-9694-4

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  • DOI: https://doi.org/10.1007/s00233-015-9694-4

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