Remarks on Weierstrass 6-semigroups
Main Article Content
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
Article Details
Copyright Transfer Statement
The copyright of this article is transferred to Current Applied Science and Technology journal with effect if and when the article is accepted for publication. The copyright transfer covers the exclusive right to reproduce and distribute the article, including reprints, translations, photographic reproductions, electronic form (offline, online) or any other reproductions of similar nature.
The author warrants that this contribution is original and that he/she has full power to make this grant. The author signs for and accepts responsibility for releasing this material on behalf of any and all co-authors.
Here is the link for download: Copyright transfer form.pdf
References
[2] J. Herzog, Generators and relations of abelian semigroups and semigroup rings. Manuscripta Math. 3 (1970), 175-193.
[3] A. Hurwitz, Über algebraischer Gebilde mit eindeutigen Transformationen in sich. Math. Ann. 41 (1893), 403-442.
[4] S.J. Kim and J. Komeda, Weierstrass semigroups of a pair of points whose first nongaps are three. Geometriae Dedicata 93 (2002), 113-119.
[5] S.J. Kim and J. Komeda, The Weierstrass semigroups of a pair of Galois Weierstrass points with prime degree on a curve. Preprint.
[6] J. Komeda, On Weierstrass points shoes first non-gaps are four. J. Reine Angrew. Math. 341 (1983), 68-86.
[7] J. Komeda, On the existence of Weierstrass points whose first non-gaps are five. Manuscripta Math. 76 (1992), 193-211.
[8] J. Komeda, Cyclic coverings of an elliptic curve with two branch points and the gap sequences at the ramification points. Acta Arithmetica LXXI (1997), 275-297.
[9] J. Komeda and A. Ohbuchi, The existence of a double covering of a curve with a certain Weierstrass point. Preprint
[10] C. Maclachlan, Weierstrass points on compact Riemann surfaces. J. London Math. Soc. 3 (1971), 722-724.