Remarks on Weierstrass 6-semigroups
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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
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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.
