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.
- Giulietti–Korchmáros maximal curve
- Weierstrass points
- Weierstrass semigroup