Double coverings of curves and non-Weierstrass semigroups
Double coverings of curves and non-Weierstrass semigroups
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曲线和非魏尔斯特拉斯半群的双重覆盖
DOI：
10.1080/00927872.2011.629324
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发表时间：
2013
影响因子：
0.7
通讯作者：
Jiryo Komeda
中科院分区：
文献类型：
--
作者：
Jiryo Komeda;Shigeki Matsutani; Emma Previato;大杉英史，日比孝之;Jiryo Komeda
给出了构造特征为0且Weierstrass半群为H的非Weierstrass半群H的一种新方法，即在特征为0的代数闭域上不存在光滑投影点曲线，该方法依赖于对光滑投影点曲线的描述，使得该曲线在点上分支存在双覆盖，且覆盖曲线的格上有一定的条件。利用这一方法，我们找到了最小正整数分别为8和12的非weierstrass半群。
We give a new method of constructing a non-Weierstrass semigroup H, which means that there is no smooth projective pointed curve over an algebracally closed field of characteristic 0 whose Weierstrass semigroup is H. This method depends on a description of a pointed smooth projective curve such that there exists a double covering of the curve ramified over the point with a certain condition on the genus of the covering curve. Using this we find non-Weierstrass semigroups whose minimum positive integers are 8 and 12, respectively.