Non-K3 Weierstrass numerical semigroups

IF 0.7 3区数学 Q2 MATHEMATICS Semigroup Forum Pub Date : 2024-02-07 DOI:10.1007/s00233-024-10406-0

Jiryo Komeda, Makiko Mase

引用次数: 0

Abstract

We generalize the result of Reid (J Lond Math Soc 13:454–458, 1976), namely, we prove that a curve of genus $\geqq g^2+4g+6$ having a double cover of a hyperelliptic curve of genus $g\geqq 2$ does not lie as a non-singular curve on any K3 surface. Applying this result we construct non-K3 Weierstrass numerical semigroups. A numerical semigroup H is said to be Weierstrass if there exists a pointed non-singular curve (C, P) such that H consists of non-negative integers which are the pole orders at P of a rational function on C having a pole only at P. We call the numerical semigroup K3 if we can take the curve C as a curve on some K3 surface. A non-K3 numerical semigroup means that it cannot be attained by a pointed non-singular curve on any K3 surface. We also give infinite sequences of non-K3 Weierstrass numerical semigroups.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

非 K3 Weierstrass 数字半群

我们概括了里德（J Lond Math Soc 13:454-458, 1976）的结果，即我们证明了具有双盖的属（g/geqq g^2+4g+6\ ）超椭圆曲线的属（g/geqq 2\ ）的曲线不作为非星形曲线位于任何 K3 曲面上。应用这一结果，我们构造了非 K3 Weierstrass 数字半群。如果存在一条尖的非星形曲线 (C，P)，使得 H 由非负整数组成，而这些非负整数是 C 上的有理函数在 P 处的极值阶，且该有理函数仅在 P 处有一个极值，则称该数值半群为魏尔斯特拉斯数值半群。非 K3 数值半群意味着它不能由任何 K3 曲面上的一条尖的非星形曲线达到。我们还给出了非 K3 魏尔斯特拉斯数值半群的无限序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Semigroup Forum 数学-数学

CiteScore

1.50

自引率

14.30%

发文量

审稿时长

12 months

期刊介绍： Semigroup Forum is a platform for speedy and efficient transmission of information on current research in semigroup theory. Scope: Algebraic semigroups, topological semigroups, partially ordered semigroups, semigroups of measures and harmonic analysis on semigroups, numerical semigroups, transformation semigroups, semigroups of operators, and applications of semigroup theory to other disciplines such as ring theory, category theory, automata, logic, etc. Languages: English (preferred), French, German, Russian. Survey Articles: Expository, such as a symposium lecture. Of any length. May include original work, but should present the nonspecialist with a reasonably elementary and self-contained account of the fundamental parts of the subject. Research Articles: Will be subject to the usual refereeing procedure. Research Announcements: Description, limited to eight pages, of new results, mostly without proofs, of full length papers appearing elsewhere. The announcement must be accompanied by a copy of the unabridged version. Short Notes: (Maximum 4 pages) Worthy of the readers'' attention, such as new proofs, significant generalizations of known facts, comments on unsolved problems, historical remarks, etc. Research Problems: Unsolved research problems. Announcements: Of conferences, seminars, and symposia on Semigroup Theory. Abstracts and Bibliographical Items: Abstracts in English, limited to one page, of completed work are solicited. Listings of books, papers, and lecture notes previously published elsewhere and, above all, of new papers for which preprints are available are solicited from all authors. Abstracts for Reviewing Journals: Authors are invited to provide with their manuscript informally a one-page abstract of their contribution with key words and phrases and with subject matter classification. This material will be forwarded to Zentralblatt für Mathematik.

期刊最新文献

Presentation of monoids generated by a projection and an involution Tropical representations of Chinese monoids with and without involution Conditionally distributive uninorms locally internal on the boundary A characterization of piecewise $$\mathscr {F}$$ -syndetic sets On the monoid of order-preserving transformations of a finite chain whose ranges are intervals