The proportion of Weierstrass semigroups
The proportion of Weierstrass semigroups
复制标题
维尔斯特拉斯半群的比例
DOI：
10.1016/j.jalgebra.2012.09.041
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发表时间：
2012
影响因子：
0.9
通讯作者：
Lynnelle Ye
中科院分区：
文献类型：
--
作者：
N. Kaplan;Lynnelle Ye
我们解决了 Komeda 问题，涉及不满足 Buchweitz 半群作为代数曲线上点的 Weierstrass 半群出现的必要标准的数值半群的比例。艾森巴德和哈里斯的结果给出了半群作为维尔斯特拉斯半群出现的充分条件。我们证明满足这个条件的半群族在所有半群的集合中密度为零。在此过程中，我们证明了关于典型数值半群结构的几个更一般的结果。
We solve a problem of Komeda concerning the proportion of numerical semigroups which do not satisfy Buchweitzʼ necessary criterion for a semigroup to occur as the Weierstrass semigroup of a point on an algebraic curve. A result of Eisenbud and Harris gives a sufficient condition for a semigroup to occur as a Weierstrass semigroup. We show that the family of semigroups satisfying this condition has density zero in the set of all semigroups. In the process, we prove several more general results about the structure of a typical numerical semigroup.