Mathematical Sciences: Algebra Structures on Resolutions andGorenstein Ideals

本课题主要研究循环模的自由分解的代数结构。主要研究者将研究循环模的最小分解上的代数结构的存在性。她还将确定在完全交的联结类中由理想定义的代数的最小分解是否允许导致代数结构的乘法。这项工作是关于交换代数和代数几何界面上的数学。要研究的特殊问题是这一非常活跃的数学领域的核心。

This project is concerned with the study of algebra structures on free resolutions of cyclic modules. The principal investigator will study the existence of an algebra structure on the minimal resolution of a cyclic module. She will also determine if the minimal resolution of the algebras defined by ideals in the linkage class of a complete intersection admit a multiplication leading to an algebra structure. This work is concerned with mathematics on the interface of commutative algebra and algebraic geometry. The particular problems to be investigated are central to this very active area of mathematics.