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

Authors
Cheon, Eun JuKim, Seon Jeong
Issue Date
Nov-2020
Publisher
KOREAN SOC MATHEMATICAL EDUCATION
Keywords
Weierstrass point; Weierstrass semigroup at a pair; Weierstrass semigroup at a point; quadratic curve; conic
Citation
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS, v.27, no.4, pp.251 - 267
Indexed
KCI
Journal Title
JOURNAL OF THE KOREAN SOCIETY OF MATHEMATICAL EDUCATION SERIES B-PURE AND APPLIED MATHEMATICS
Volume
27
Number
4
Start Page
251
End Page
267
URI
https://scholarworks.bwise.kr/gnu/handle/sw.gnu/6021
DOI
10.7468/jksmeb.2020.27.4.251
ISSN
1226-0657
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.
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