Mathematical Sciences: Topics in Commutative Algebra and Algebraic Geometry

数学科学：交换代数和代数几何主题

• 批准号: 9106739
• 负责人: Roger Wiegand
• 金额: $ 1.71万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-06-01 至 1993-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9106739&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Topics; Commutative; Algebra

This project supports research in commutative algebra and algebraic geometry. The principal investigators will study torsion-free, projective and Cohen-Macaulay modules over affine rings and their localizations; prime ideal structure of two-dimensional affine domains; and Hilbert functions and reduction numbers of primary ideals in Cohen-Macaulay local rings. They will also consider automorphism groups of rational surfaces; ideal theoretic questions of embedded rational surfaces; and the set-theoretic complete intersection problem for curves in projective 3-space. Algebraic geometry is the study of the geometric objects arising from the sets of zeros of systems of polynomial equations. This is one of the oldest and currently one of the most active branches of mathematics. It has widespread applications in mathematics, computer science and physics.

该项目支持交换代数和代数几何的研究。 主要研究人员将研究仿射环上的无扭模、射影模和科恩-麦考利模及其定位；二维仿射域的素理想结构；和 Hilbert 函数以及 Cohen-Macaulay 局部环中初等理想的约简数。 他们还将考虑有理曲面的自同构群；嵌入有理面的理想理论问题；以及射影三空间中曲线的集合论完全相交问题。 代数几何是对多项式方程组零点集产生的几何对象的研究。 这是数学最古老的分支之一，也是目前最活跃的数学分支之一。 它在数学、计算机科学和物理学中有着广泛的应用。