Mathematical Sciences: Free Resolutions in Commutative Algebra

这个项目是关于自由决议。 的 主要研究人员将研究有限分辨率， 特别强调乘法结构， 支持及其在联系理论中的作用。 家属 将研究解决方案，包括对象的解决方案 例如完全交集的连接类中的代数， 由剩余交和完全幂定义的代数 理想、规范类和其他类组元素，以及 模的有限长度在环的固定尺寸。 代数几何是研究几何对象的科学 由多项式系统的零点集引起的 方程 这是一个最古老的，目前的一个 最活跃的数学分支。 它广泛传播 数学、计算机科学和物理学的应用。

This project is concerned with free resolutions. The principal investigators will study finite resolutions, with particular emphasis on the multiplicative structures they may support and their role in linkage theory. Families of resolutions will be investigated including resolutions of objects such as algebras in the linkage class of a complete intersection, algebras defined by residual intersections and powers of perfect ideals, canonical classes and other class group elements, and modules of finite length over rings of a fixed dimension. 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.