Bounds for syzygies of monomial curves

IF 0.8 3区数学 Q2 MATHEMATICS

Proceedings of the American Mathematical Society Pub Date : 2024-04-03 DOI:10.1090/proc/16862

Giulio Caviglia, Alessio Moscariello, Alessio Sammartano

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引用次数: 0

Abstract

Let Γ ⊆ N \Gamma \subseteq \mathbb {N} be a numerical semigroup. In this paper, we prove an upper bound for the Betti numbers of the semigroup ring of Γ \Gamma which depends only on the width of Γ \Gamma , that is, the difference between the largest and the smallest generator of Γ \Gamma . In this way, we make progress towards a conjecture of Herzog and Stamate [J. Algebra 418 (2014), pp. 8–28]. Moreover, for 4-generated numerical semigroups, the first significant open case, we prove the Herzog-Stamate bound for all but finitely many values of the width.

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单项式曲线对称性的界限

让 Γ ⊆ N \Gamma \subseteq \mathbb {N} 是一个数字半群。在本文中，我们证明了 Γ \Gamma 的半群环的贝蒂数的上界，它只取决于 Γ \Gamma 的宽度，即 Γ \Gamma 的最大生成器和最小生成器之间的差值。这样，我们在实现赫尔佐格和斯塔马特的猜想方面取得了进展[《代数学杂志》418 (2014)，第 8-28 页]。此外，对于 4 代数值半群--第一个重要的开放情形--我们证明了赫尔佐格-斯塔马特对除有限多个宽度值之外的所有宽度值的约束。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to shorter research articles (not to exceed 15 printed pages) in all areas of pure and applied mathematics. To be published in the Proceedings, a paper must be correct, new, and significant. Further, it must be well written and of interest to a substantial number of mathematicians. Piecemeal results, such as an inconclusive step toward an unproved major theorem or a minor variation on a known result, are in general not acceptable for publication. Longer papers may be submitted to the Transactions of the American Mathematical Society. Published pages are the same size as those generated in the style files provided for AMS-LaTeX.