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
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