Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DOUBLE COVERS OF PLANE CURVES OF DEGREE SIX WITH ALMOST TOTAL FLEXES

  • Kim, Seon Jeong (Department of Mathematics and RINS Gyeongsang National University) ;
  • Komeda, Jiryo (Department of Mathematics Center for Basic Education and Integrated Learning Kanagawa Institute of Technology)
  • Received : 2018.09.27
  • Accepted : 2019.04.25
  • Published : 2019.09.30
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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.

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References

  1. T. Harui and J. Komeda, Numerical semigroups of genus eight and double coverings of curves of genus three, Semigroup Forum 89 (2014), no. 3, 571-581. https://doi.org/10.1007/s00233-014-9590-3
  2. S. J. Kim and J. Komeda, Weierstrass semigroups on double covers of genus 4 curves, J. Algebra 405 (2014), 142-167. https://doi.org/10.1016/j.jalgebra.2014.02.006
  3. S. J. Kim and J. Komeda, Weierstrass semigroups on double covers of plane curves of degree 5, Kodai Math. J. 38 (2015), no. 2, 270-288. https://doi.org/10.2996/kmj/1436403890
  4. S. J. Kim and J. Komeda, Weierstrass semigroups on double covers of plane curves of degree six with total flexes, Bull. Korean Math. Soc. 55 (2018), no. 2, 611-624. https://doi.org/10.4134/BKMS.b170195