Mathematical Sciences: Free Resolutions in Commutative Algebra

这个项目是与自由决议有关的。主要研究人员将研究有限分辨率，特别强调它们可能支持的乘法结构及其在链接理论中的作用。我们将研究一族分解，包括对象的分解，如完全交的链类中的代数，由剩余交和完全理想的幂、标准类和其他类群元定义的代数，以及固定维环上的有限长度的模。代数几何是研究由多项式方程组的零点集产生的几何对象的学科。这是最古老的，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。

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.