参考文献:1. Garcia, A (1986) Weights of Weierstrass points in double coverings of curves of genus one or two. Manuscripta Math. 55: pp. 419-432 CrossRef 2. Harui, T., Komeda, J.: Numerical semigroups of genus eight and double coverings of curves of genus three, to appear in Semigroup Forum 3. Harui, T., Komeda, J., Ohbuchi, A.: The Weierstrass semigroups on double covers of genus two curves, preprint 4. Komeda, J (2009) A numerical semigroup from which the semigroup gained by dividing by two is either $$\mathbb{N}_0$$ N 0 or a 2-semigroup or $$\langle 3,4,5 \rangle $$ 鉄3 , 4 , 5 鉄? Res. Rep. Kanagawa Inst. Technol. B鈥?3: pp. 37-42 5. Komeda, J (2011) On Weierstrass semigroups of double coverings of genus three curves. Semigroup Forum 83: pp. 479-488 CrossRef 6. Komeda, J, Ohbuchi, A (2004) Weierstrass points with first non-gap four on a double covering of a hyperelliptic curve. Serdica Math. J. 30: pp. 43-54 7. Komeda, J, Ohbuchi, A (2008) Weierstrass points with first non-gap four on a double covering of a hyperelliptic curve II. Serdica Math. J. 34: pp. 771-782 8. Oliveira, G, Pimentel, FLR (2008) On Weierstrass semigroups of double covering of genus two curves. Semigroup Forum 77: pp. 152-162 CrossRef 9. Oliveira, G, Torres, F, Villanueva, J (2010) On the weight of numerical semigroups. J. Pure Appl. Algebra 214: pp. 1955-1961 CrossRef
刊物类别:Mathematics and Statistics
刊物主题:Mathematics Algebra
出版者:Springer New York
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 seven, and prove that all of such numerical semigroups are actually of double covering type.