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

所涉及的研究是在两个不同但相关的领域 局部交换代数一个领域是系统研究 局部上同调较小的局部环中参数的 模块具有有限的长度和爆破的效果， 由这样的参数系统产生的理想。第二 面积是研究极小双有理正则局部环， 与理想的正则闭包的关系。 本项目涉及的接口的研究 交换代数和代数几何。给定曲线， 交换代数可以与之相关联。信息 从研究交换代数用品 关于曲线的信息这是一个发展迅速的领域 影响了数学的许多领域。

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.