Weierstrass semigroups on the Giulietti–Korchmáros curve

Peter Beelen*, Maria Montanucci

*Corresponding author for this work

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Abstract

In this article we explicitly determine the structure of the Weierstrass semigroups H(P) for any point P of the Giulietti–Korchmáros curve X. We show that as the point varies, exactly three possibilities arise: one for the Fq2 -rational points (already known in the literature), one for the Fq6 ∖Fq2 -rational points, and one for all remaining points. As a result, we prove a conjecture concerning the structure of H(P) in case P is an Fq6 ∖Fq2 -rational point.
Original languageEnglish
JournalFinite Fields and Their Applications
Volume52
Pages (from-to)10-29
ISSN1071-5797
DOIs
Publication statusPublished - 2018

Keywords

  • Giulietti–Korchmáros maximal curve
  • Weierstrass points
  • Weierstrass semigroup

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