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

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In this paper, we study Weierstrass semigroups of ramification points on double covers of plane curves of degree $6$. We determine all the Weierstrass semigroups when the genus of the covering curve is greater than $29$ and the ramification point is on a total flex.

Abstract

In this paper, we study Weierstrass semigroups of ramification points on double covers of plane curves of degree $6$. We determine all the Weierstrass semigroups when the genus of the covering curve is greater than $29$ and the ramification point is on a total flex.

참고문헌 (7)

  1. T. Harui, "Numerical semigroups of genus eight and double coverings of curves of genus three", Semigroup Forum, 89(3), pp.571~581 (2014)
  2. T. Harui, "Numerical semigroups of genus seven and double coverings of curves of genus three", Semigroup Forum, 90(2), pp.491~502 (2015)
  3. T. Harui, "Numerical semigroups of genus six and double coverings of curves of genus three", Semigroup Forum, 91(3), pp.601~610 (2015)
  4. S. J. Kim, "Weierstrass semigroups on double covers of genus 4 curves", J. Algebra, 405, pp.142~167 (2014)[DOI]
  5. S. J. Kim, "Weierstrass semigroups on double covers of plane curves of degree 5", Kodai Math. J., 38(2), pp.270~288 (2015)[DOI]
  6. A numerical semigroup from which the semigroup gained by dividing by two is either <TEX>$\mathbb-N}_0$<, "TEX> or a 2-semigroup or <3, 4, 5>, Research Reports of Kanagawa Institute of Technology B-33", J. Komeda, 2009, pp.37~42
  7. J. Komeda, "On Weierstrass semigroups of double coverings of genus three curves", Semigroup Forum, 83(3), pp.479~488 (2011)

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