Syzygies

赛兹吉斯

• 批准号: 1100046
• 负责人: Irena Peeva
• 金额: $ 21.85万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2014-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1100046&HistoricalAwards=false
• 关键词: Syzygies

This project is in the field of commutative algebra. The main research goal is to understand the structure of minimal free resolutions over complete intersection ring. The idea is to describe the asymptotic structure of the generic Eisenbud operators, and then use it in order to obtain the differentials. The proposed research also includes a topic involving interdisciplinary approaches connecting commutative algebra with the fields of combinatorics and topology. The PI will co-organize two conferences in commutative algebra, which will provide a forum for discussion of recent developments and foster research in new directions.Research on free resolutions is a core and beautiful area in commutative algebra. It contains a number of challenging and important conjectures and open problems. The idea to associate a free resolution to a finitely generated module was introduced by Hilbert in two famous papers in 1890 and 1893. He proved that over a polynomial ring (over a field) every finitely generated module has a finite resolution. In the local and the graded cases there exists a minimal free resolution; it is unique up to an isomorphism and is contained in any free resolution of the resolved module. Its properties are closely related to the invariants of the resolved module. For many years, minimal free resolutions have been both central objects and fruitful tools in Commutative Algebra; they also have applications in other mathematical fields.

该项目位于交换代数的领域。主要的研究目标是了解完整交叉路口的最小自由分辨率的结构。这个想法是描述通用Eisenbud操作员的渐近结构，然后使用它来获得差异。拟议的研究还包括一个涉及跨学科方法的主题，该方法将交换代数与组合学和拓扑结构相关联。 PI将在交换代数中共同组织两个会议，该会议将为讨论新方向的最新发展和促进研究提供一个论坛。搜索自由决议是通勤代数的核心和美丽的领域。它包含许多具有挑战性和重要的猜想和开放问题。希尔伯特（Hilbert）在1890年和1893年的两篇著名论文中引入了将自由分辨率与有限生成的模块相关联的想法。他证明，每个有限生成的模块都具有有限的分辨率。在本地和分级案例中，存在最少的自由分辨率；它是唯一的同构，并且包含在已解决模块的任何自由分辨率中。它的属性与已解决模块的不变性密切相关。多年来，最少的自由决议既是通勤代数的中心物品，也是富有成果的工具。他们在其他数学领域也有应用。