Mathematical Sciences: Structure of Projective Modules and Generation of Ideals over Affine Rings

这个项目是关于交换 代数 首席研究员将调查结构 投射模和理想的有效生成， 仿射代数上的模 我们的目标是研究这些问题 通过将合适的不变量附加到投射模和理想上。 这些不变量来自仿射簇的几何 附在戒指上。 一个突出的作用是由周 仿射簇群和射影的陈类 模块。 这项研究是在一般领域的代数几何。 代数几何是研究几何对象产生的 多项式方程组的零点集。 这是一 最古老也是目前最活跃的分支之一 数学 它在数学中有着广泛的应用， 计算机科学和物理学。

This project is concerned with research in commutative algebra. The principal investigator will investigate the structure of projective modules and the efficient generation of ideals and modules over affine algebras. The goal is to study these problems by attaching suitable invariants to projective modules and ideals. These invariants arise from the geometry of the affine variety attached to the ring. A prominent role is played by the Chow groups of the affine varieties and the Chern classes of projective modules. This research is in the general area of algebraic geometry. Algebraic geometry is the study of 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.