• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.353-368
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• 2022

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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.399-411
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• 2021

We consider a Weierstrass semigroup at a generalized flex on a smooth plane curve. We find the candidates of a Weierstrass semigroup at a 2-flex of higher multiplicity on a smooth plane curve of degree d ≥ 5, and give some examples to show the existence of them.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권4호
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• pp.251-267
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• 2020

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.

• 대한수학회보
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• 제44권2호
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• pp.369-378
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• 2007

We classify all semigroups each of which arises as a Weierstrass semigroup at a pair of inflection points of multiplicities d or d-1 on a smooth plane curve of degree d.

• 대한수학회지
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• 제56권6호
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• pp.1463-1474
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• 2019

Let C be a nonsingular projective curve of genus ${\geq}2$ over an algebraically closed field of characteristic 0. For a point P in C, the Weierstrass semigroup H(P) is defined as the set of non-negative integers n for which there exists a rational function f on C such that the order of the pole of f at P is equal to n, and f is regular away from P. A point P in C is referred to as a weak Galois-Weierstrass point if P is a Weierstrass point and there exists a Galois morphism ${\varphi}:C{\rightarrow}{\mathbb{p}}^1$ such that P is a total ramification point of ${\varphi}$. In this paper, we investigate the number of weak Galois-Weierstrass points of which the Weierstrass semigroups are generated by two positive integers.

• 대한수학회지
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• 제32권4호
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• pp.753-759
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• 1995

Let C be a smooth complex algebraic curve of genus g. For a divisor D on C, dim D means the dimension of the complete linear series $\mid$D$\mid$ containing D, which is the same as the projective dimension of the vector space of meromorphic functions f on C with divisor of poles $(f)_\infty \leq D$.