Homology of Monomial and Toric Ideals

单项式和环面理想的同调

• 批准号: 9970334
• 负责人: Irena Peeva
• 金额: $ 6.34万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-07-01 至 2001-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9970334&HistoricalAwards=false
• 关键词: Homology; Monomial; Toric; Ideals

ABSTRACTIrena PeevaDMS-9970334Dr. Peeva will work on projects in the general area of Commutative Algebra. Her project deals with the structure of the minimal free resolutions of Monomial and Toric ideas. Ideas and methods from commutative algebra, combinatorics, and the topological theory of subspace arrangements will be applied to study such resolutions. Constructions previously used to describe the cohomology of complex subspace arrangements will be adapted to yield minimal free resolutions. The goal is to build highly structured resolutions and subcomplexes of resolutions, and to obtain bounds on Betti Numbers and regularity. Commutative algebra is the study of the fundamental structures of mathematics. Results of commutative algebra have found uses in communications, security and robotics. By studying abstract mathematical objects, mathematicians gain deeper insight in many other branches of mathematics. The important area of modern geometry known as algebraic geometry is the strongest and most fruitful mathematical example of this line of attack. Algebraic objects are substituted for geometric objects, and the powerful and abstract methods of commutative algebra are applied to further our understanding of the geometry. Dr. Peeva's research should have immediate and direct implications in geometry and combinatorics.

Abstractirena peevadms-9970334dr。 Peeva将在交换代数的一般领域从事项目。 她的项目涉及最少的单一思想和曲折思想的自由决议的结构。 可交换代数，组合学和子空间排列拓扑理论的思想和方法将应用于研究此类决议。 先前用于描述复杂子空间排列的共同体的结构将适应最少的自由分辨率。目的是建立高度结构化的分辨率和分辨率的子复合，并在Betti数字和规律性方面获得界限。 交换代数是对数学基本结构的研究。换向代数的结果发现了通信，安全和机器人技术的用途。通过研究抽象数学对象，数学家在许多其他数学分支中获得了更深入的见解。称为代数几何形状的现代几何形状的重要领域是这种攻击线的最强，最富有成果的数学例子。 代数对象被替换为几何对象，并应用了有力和抽象的代数方法，以进一步了解我们对几何形状的理解。 Peeva博士的研究应在几何和组合学上具有直接和直接的影响。