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  • 한국과학기술정보연구원(KISTI) 서울분원 대회의실(별관 3층)
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ISSN : 1226-0657

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Vol.27 No.4

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WEIERSTRASS SEMIGROUPS AT PAIRS OF NON-WEIERSTRASS POINTS ON A SMOOTH PLANE CURVE OF DEGREE 5

WEIERSTRASS SEMIGROUPS AT PAIRS OF NON-WEIERSTRASS POINTS ON A SMOOTH PLANE CURVE OF DEGREE 5

한국수학교육학회지시리즈B:순수및응용수학 / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2020, v.27 no.4, pp.251-267
https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.4.251
Cheon, Eun Ju (Department of Mathematics and RINS, Gyeongsang National University)
Kim, Seon Jeong (Department of Mathematics and RINS, Gyeongsang National University)
Cheon, Eun Ju, & Kim, Seon Jeong. (2020). WEIERSTRASS SEMIGROUPS AT PAIRS OF NON-WEIERSTRASS POINTS ON A SMOOTH PLANE CURVE OF DEGREE 5. 한국수학교육학회지시리즈B:순수및응용수학, 27(4), 251-267, https://doi.org/https://doi.org/10.7468/jksmeb.2020.27.4.251

Abstract

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of non-Weierstrass points on a smooth plane curve of degree 5. First we find the candidates of semigroups by computing the dimensions of linear series on the curve. Then, by constructing examples of smooth plane curves of degree 5, we prove that each of the candidates is actually a Weierstrass semigroup at some pair of points on the curve. We need to study the systems of quadratic curves, which cut out the canonical series on the plane curve of degree 5.

keywords
Weierstrass point, Weierstrass semigroup at a pair, Weierstrass semigroup at a point, quadratic curve, conic

한국수학교육학회지시리즈B:순수및응용수학

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