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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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / 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
Kim, Seon Jeong
Cheon,, E. J. , & Kim,, S. J. (2020). WEIERSTRASS SEMIGROUPS AT PAIRS OF NON-WEIERSTRASS POINTS ON A SMOOTH PLANE CURVE OF DEGREE 5. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 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

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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