Topics in commutative algebra

交换代数主题

• 批准号: 2264817
• 金额: --
• 依托单位: University of Sheffield
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2264817
• 关键词: Topics; commutative; algebra

BETTI NUMBERS STANLEY REISNER IDEALSAny graded, finitely generated module affords a minimal graded resolution, and these resolutions provide a wealth of information about the original module. One such piece of information are the Betti numbers of the module; these are the degrees of the free generators in a minimal free resolution.One of the most exciting recent developments in commutative algebra is the emergence of the Boij-Soderberg Theory which describes the convex cone generated by all the Betti numbers of Cohen-Macaulay modules over a polynomial ring, in particular it describes the extremal rays of this cone and ways to express any given betti diagram as a convex combination of points on these rays.David Carey's project studies the subcone generated by Betti diagrams of square free monomial ideals in general, and edge ideals in particular. The aim of the project is to exploit the combinatorial structure of these ideals to gain an understanding of the betti cones, e.g., the classification of extremal rays in the Betti cones of edge ideals in terms of the properties of the underlying graphs.

贝蒂数斯坦利·赖斯纳理想任何分级的、可重构的模块都提供了一个最小的分级分辨率，这些分辨率提供了关于原始模块的丰富信息。一个这样的信息片段是模块的贝蒂数;交换代数中最近最令人兴奋的发展之一是Boij-Soderberg理论的出现，该理论描述了多项式环上Cohen-Macaulay模的所有Betti数生成的凸锥，特别是它描述了极值射线这个锥和方式来表达任何给定的贝蒂图作为一个凸组合的点在这些rais.大卫凯里的项目研究的子锥所产生的贝蒂图的平方自由单项理想一般，特别是边缘理想。该项目的目的是利用这些理想的组合结构来理解贝蒂锥，例如，根据基本图的性质对边理想的Betti锥中的极值射线进行分类。

项目成果

Dimensions of Betti Cones on Edge Ideals

• DOI: 10.1016/j.jpaa.2022.107054
• 发表时间: 2021-04
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: David Carey