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Weierstrass semigroups on double covers of plane curves of degree six with total flexes. (English) Zbl 1401.14158
The 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)].

MSC:
14H55 Riemann surfaces; Weierstrass points; gap sequences
14H50 Plane and space curves
14H30 Coverings of curves, fundamental group
20M14 Commutative semigroups
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References:
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