Mathematical Sciences: Finite Local Cohomology Rings and Minimally Regular Local Rings

所涉及的研究是在局部交换代数的两个不同但相关的领域。一个领域是研究较小的局部上同模具有有限长度的局部环上的参数系统，以及由参数系统产生的理想的吹胀对这种系统的影响。第二个领域是最小双族正则局部环和理想正则闭包连接的研究。本课题涉及交换代数与代数几何的界面研究。给定一条曲线，交换代数可以与它联系起来。研究交换代数得到的信息提供了关于曲线的信息。这是一个迅速发展的领域，影响着数学的许多领域。

The research involved is in two distinct but related areas of local commutative algebra. One area is the study of systems of parameters in local rings whose smaller local cohomology modules have finite length and the effect of blowing-up an ideal generated by a system of parameters on such. The second area is the study of minimal birational regular local rings and connections with the regular closure of ideals. This project involves research on the interface of commutative algebra and algebraic geometry. Given a curve, a commutative algebra can be associated with it. Information derived from studying the commutative algebra supplies information about the curve. This is a rapidly developing area which impacts many areas of mathematics.