Mathematical Sciences: Topics in Commutative Algebra and Algebraic Geometry

该项目支持交换代数的研究， 代数几何 主要研究人员将研究 仿射上无挠、投射和Cohen-Macaulay模 环及其局部化;素理想结构 二维仿射域;希尔伯特函数和约化 Cohen-Macaulay局部环中准素理想的个数 他们将 也考虑有理曲面的自同构群;理想 嵌入有理曲面的理论问题; 中曲线的集合论完全交问题 射影三维空间 代数几何是研究几何对象的科学 由多项式方程组的零点集合产生。 这是一个最古老的，目前最活跃的 数学的分支。 它具有广泛的应用， 数学、计算机科学和物理学。

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.