• The Pure and Applied Mathematics
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• v.29 no.4
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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.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.403-412
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• 2015

Kato[6] and Torres[9] characterized the Weierstrass semigroup of ramification points on h-hyperelliptic curves. Also they showed the converse results that if the Weierstrass semigroup of a point P on a curve C satisfies certain numerical condition then C can be a double cover of some curve and P is a ramification point of that double covering map. In this paper we expand their results on the Weierstrass semigroup of a ramification point of a double covering map to the Weierstrass semigroup of a pair (P, Q). We characterized the Weierstrass semigroup of a pair (P, Q) which lie on the same fiber of a double covering map to a curve with relatively small genus. Also we proved the converse: if the Weierstrass semigroup of a pair (P, Q) satisfies certain numerical condition then C can be a double cover of some curve and P, Q map to the same point under that double covering map.

• The Pure and Applied Mathematics
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• v.27 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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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.

• Journal of the Korean Mathematical Society
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• v.32 no.4
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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 $(f)_\infty \leq D$.