Weierstrass semigroups on the Giulietti–Korchmáros curve

Peter  Beelen; Maria Montanucci

doi:10.1016/j.ffa.2018.03.002

Weierstrass semigroups on the Giulietti–Korchmáros curve

Peter Beelen^*, Maria Montanucci

^*Corresponding author for this work

University of Basilicata

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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 language	English
Journal	Finite Fields and Their Applications
Volume	52
Pages (from-to)	10-29
ISSN	1071-5797
DOIs	https://doi.org/10.1016/j.ffa.2018.03.002
Publication status	Published - 2018

Keywords

Giulietti–Korchmáros maximal curve
Weierstrass points
Weierstrass semigroup

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10.1016/j.ffa.2018.03.002

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title = "Weierstrass semigroups on the Giulietti–Korchm{\'a}ros curve",

abstract = "In this article we explicitly determine the structure of the Weierstrass semigroups H(P) for any point P of the Giulietti–Korchm{\'a}ros 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.",

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author = "Peter Beelen and Maria Montanucci",

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language = "English",

volume = "52",

pages = "10--29",

journal = "Finite Fields and Their Applications",

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T1 - Weierstrass semigroups on the Giulietti–Korchmáros curve

AU - Beelen, Peter

AU - Montanucci, Maria

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Giulietti–Korchmáros maximal curve

KW - Weierstrass points

KW - Weierstrass semigroup

U2 - 10.1016/j.ffa.2018.03.002

DO - 10.1016/j.ffa.2018.03.002

M3 - Journal article

SN - 1071-5797

VL - 52

SP - 10

EP - 29

JO - Finite Fields and Their Applications

JF - Finite Fields and Their Applications

ER -

Weierstrass semigroups on the Giulietti–Korchmáros curve

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Keywords

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