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On the existence of Weierstrass points whose first non-gaps are five

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Abstract

LetH be a numerical semigroup, i.e., a subsemigroup of the additive semigroup N of non-negative integers whose complement N/H in N is finite. Leta be the least positive integer inH. Then we show that ifa=5, then there exists a pointed complete non-singular irreducible algebraic curve (C, P) such thatH is the set of integers which are pole orders atP of regular functions onC/{P}.

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  1. Kanagawa Institute of Technology, 1030 Shimo-Ogino, Atsugi-shi, 243-02, Kanagawa, Japan

    Jiryo Komeda

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  1. Jiryo Komeda
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Komeda, J. On the existence of Weierstrass points whose first non-gaps are five. Manuscripta Math 76, 193–211 (1992). https://doi.org/10.1007/BF02567755

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  • DOI: https://doi.org/10.1007/BF02567755

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