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Remarks on Weierstrass 6-semigroups

Remarks on Weierstrass 6-Semigroups

Original Research ArticleNov 12, 2018Vol. 5 No. 1 (2005)

Abstract

A numerical semigroup means a subsemigroup of the additive semigroup ℕ0 consisting of non-negative integers such that its complement in ℕ0 is finite. A numerical semigroup H is called an n-semigroup if the minimum positive integer in H is n. A numerical semigroup is said to be Weierstrass if it is the set H (P) which consists of pole orders at P of regular functions on C\ {P} for some pointed non-singular curve (C, P). This paper is devoted to the study of Weierstrass 6-semigroups H. Especially we give a Weierstrass 6-semigroup which is not the set H(P) for any ramification point P over a double covering of a non-singular curve.

Keywords: Weierstrass semigroup of a point, Cyclic Covering of the projective line, Double covering of a curve, Affine toric variety

Corresponding author: E-mail: cast@kmitl.ac.th

How to Cite

Komeda, J. . (2018). Remarks on Weierstrass 6-semigroups. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 181-189.

References

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  • A. Hurwitz, Über algebraischer Gebilde mit eindeutigen Transformationen in sich. Math. Ann. 41 (1893), 403-442.
  • S.J. Kim and J. Komeda, Weierstrass semigroups of a pair of points whose first nongaps are three. Geometriae Dedicata 93 (2002), 113-119.
  • S.J. Kim and J. Komeda, The Weierstrass semigroups of a pair of Galois Weierstrass points with prime degree on a curve. Preprint.

Author Information

Jiryo Komeda

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About this Article

Journal

Vol. 5 No. 1 (2005)

Type of Manuscript

Original Research Article

Keywords

Weierstrass semigroup of a point, Cyclic Covering of the projective line, Double covering of a curve, Affine toric variety

Published

12 November 2018