Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2019; 56(5): 1159-1186

Online first article August 6, 2019      Printed September 30, 2019

https://doi.org/10.4134/BKMS.b180915

Copyright © The Korean Mathematical Society.

Double covers of plane curves of degree six with almost total flexes

Seon Jeong Kim, Jiryo Komeda

Gyeongsang National University; Kanagawa Institute of Technology

Abstract

In this paper, we study plane curves of degree $6$ with points whose multiplicities of the tangents are $5$. We determine all the Weierstrass semigroups of ramification points on double covers of the plane curves when the genera of the covering curves are greater than $29$ and the ramification points are on the points with multiplicity $5$ of the tangent.

Keywords: numerical semigroup, Weierstrass semigroup of a point, double cover of a curve, plane curve of degree 6

MSC numbers: Primary 14H55, 14H50, 14H30, 20M14

Supported by: This work was partially supported by JPS KAKENHI Grant Numbers 18K03228 and Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education (2016R1D1A1B01011730)