Numerical semigroups of genus eight and double coverings of curves of genus three

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• 作者：Takeshi Harui (1)
  Jiryo Komeda (2)
  
• 关键词：Weierstrass semigroups ; Numerical semigroups ; Double coverings ; Plane quartics
• 刊名：Semigroup Forum
• 出版年：2014
• 出版时间：December 2014
• 年：2014
• 卷：89
• 期：3
• 页码：571-581
• 全文大小：168 KB
• 参考文献：1. Garcia, A.: Weights of Weierstrass points in double coverings of curves of genus one or two. Manuscripta Math. 55, 419鈥?32 (1986) CrossRef
  2. Harui, T., Komeda, J., Ohbuchi, A.: The Weierstrass semigroups on double covers of genus two curves (submitted)
  3. Komeda, J.: A numerical semigroup from which the semigroup gained by dividing by two is either \(\mathbb{N}_0\) or a \(2\) -semigroup or \(\langle 3,4,5 \rangle \) . Res. Rep. Kanagawa Inst. Technol. B鈥?3, 37鈥?2 (2009)
  4. Komeda, J.: On Weierstrass semigroups of double coverings of genus three curves. Semigroup Forum 83, 479鈥?88 (2011) CrossRef
  5. Komeda, J., Ohbuchi, A.: Weierstrass points with first non-gap four on a double covering of a hyperelliptic curve II. Serdica Math. J. 34, 771鈥?82 (2008)
  6. Oliveira, G., Pimentel, F.L.R.: On Weierstrass semigroups of double covering of genus two curves. Semigroup Forum 77, 152鈥?62 (2008) CrossRef
  7. Oliveira, G., Torres, F., Villanueva, J.: On the weight of numerical semigroups. J. Pure Appl. Algebra 214, 1955鈥?961 (2010) CrossRef
  
• 作者单位：Takeshi Harui (1)
  Jiryo Komeda (2)
  
  1. Academic Support Center, Kogakuin University, 2665-1 Nakano, Hachioji, Tokyo聽, 192-0015, Japan
  2. Department of Mathematics, Center for Basic Education and Integrated Learning, Kanagawa Institute of Technology, Atsugi, Kanagawa聽, 243-0292, Japan
  
• ISSN：1432-2137

文摘

The authors determine all possible numerical semigroups at ramification points of double coverings of curves when the covered curve is of genus three and the covering curve is of genus eight. Moreover, it is shown that all of such numerical semigroups are actually of double covering type.