한국수학교육학회지시리즈B:순수및응용수학 (The Pure and Applied Mathematics)

  • 제29권4호
  • /
  • Pages.353-368
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  • 2022
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  • 1226-0657(pISSN)
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  • 2287-6081(eISSN)
한국수학교육학회 (Korean Society of Mathematical Education)
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A WEIERSTRASS SEMIGROUP AT A PAIR OF INFLECTION POINTS WITH HIGH MULTIPLICITIES

  • Kim, Seon Jeong (Department of Mathematics and RINS, Gyeongsang National University) ;
  • Kang, Eunju (Department of Information and Communication Engineering, Honam University)
  • 투고 : 2022.09.07
  • 심사 : 2022.11.08
  • 발행 : 2022.11.30
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초록

In the previous paper [4], we classified the Weierstrass semigroups at a pair of inflection points of multiplicities d and d - 1 on a smooth plane curve of degree d. In this paper, as a continuation of those results, we classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d, d - 1 and d - 2 on a smooth plane curve of degree d.

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과제정보

The first author was partially supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (2022R1A2C1012291).

참고문헌

  1. M. Coppens and T. Kato: The Weierstrass gap sequence at an inflection point on a nodal plane curve, aligned inflection points on plane curves. Bollettino U.M.I. 7 (1997), no. 11-B, 1-33.
  2. M. Homma: The Weierstrass semigroup of a pair of points on a curve. Arch. Math. 67 (1996), 337-348. https://doi.org/10.1007/BF01197599
  3. E. Kang & S.J. Kim: Special pairs in the generating subset of the Weierstrass semigroup at a pair. Geom. Dedicata 99 (2003), no. 1, 167-177. https://doi.org/10.1023/A:1024960704513
  4. E. Kang & S.J. Kim: A Weierstrass semigroup at a pair of inflection points on a smooth plane curve. Bull. Korean Math. Soc. 44 (2007), no. 2, 369-378. https://doi.org/10.4134/BKMS.2007.44.2.369
  5. S.J. Kim: On the index of the Weierstrass semigroup of a pair of points on a curve. Arch. Math. 62 (1994), 73-82. https://doi.org/10.1007/BF01200442
  6. S.J. Kim & J. Komeda: Weierstrass semigroups of pairs of points whose first non-gaps are three. Geom. Dedicata 93 (2002), no. 2, 113-119 https://doi.org/10.1023/A:1020301422774