Weierstrass semigroups on double covers of plane curves of degree six with total flexes.

*(English)*Zbl 1401.14158The authors investigate Weierstrass semigroups of ramification points on double covers of plane curves of degree \(6\). The goal of the paper is to obtain all such Weierstrass semigroups when the genus of the covering curve is at least \(30\), and the ramification point is on a total flex. The proof of this main result is achieved by a detailed case-by-case study, which splits into forty-two cases. A closely related result for degree \(5\) was obtained by the authors in [Kodai Math. J. 38, No. 2, 270–288 (2015; Zbl 1327.14159)].

Reviewer: JosĂ© Javier Etayo (Madrid)

##### MSC:

14H55 | Riemann surfaces; Weierstrass points; gap sequences |

14H50 | Plane and space curves |

14H30 | Coverings of curves, fundamental group |

20M14 | Commutative semigroups |

##### Keywords:

numerical semigroup; Weierstrass semigroup of a point; double cover of a curve; plane curve of degree 6
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\textit{S. J. Kim} and \textit{J. Komeda}, Bull. Korean Math. Soc. 55, No. 2, 611--624 (2018; Zbl 1401.14158)

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##### References:

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[6] | J. Komeda, A numerical semigroup from which the semigroup gained by dividing by two is either N0or a 2-semigroup or h3, 4, 5i, Research Reports of Kanagawa Institute of Technology B-33 (2009), 37-42. 624S. J. KIM AND J. KOMEDA |

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