The proportion of Weierstrass semigroups

被引：11
|
作者：
Kaplan, Nathan [1 ]
Ye, Lynnelle [2 ]
机构：
[1] Harvard Univ, Dept Math, Cambridge, MA 02138 USA
[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA
来源：
JOURNAL OF ALGEBRA | 2013年 / 373卷
基金：
美国国家科学基金会;
关键词：
Numerical semigroup; Weierstrass semigroup; Genus of numerical semigroup; Frobenius number; NUMERICAL SEMIGROUPS;
D O I：
10.1016/j.jalgebra.2012.09.041
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We solve a problem of Komeda concerning the proportion of numerical semigroups which do not satisfy Buchweitz' 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. (C) 2012 Elsevier Inc. All rights reserved.
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页码：377 / 391
页数：15
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