Mathematical Sciences: Rees Algebras, Associated Graded Rings, and Multiple Points of Finite Morphisms

乌尔里希9623259 这个建议支持B教授的工作。乌尔里希工作的问题，在交换代数和代数几何。他打算研究Rees代数及其相关的分次环。特别是，建议的研究调查如何分次环与理想的Cohen-Macaulay性质的international。他还打算研究的问题，圈周围的经典问题，确定经典加入和割线品种的某些因素环。最后，他打算研究与完美R模和某些Cohen-Macaulay环之间的有限态射的源和目标相关的方案。 本文的研究是在交换代数与代数几何的边界上进行的。这两个领域产生于经典的问题，研究数学对象定义在平面上的最简单的方程，即多项式。今天，这些领域不仅使用代数方法，而且还使用分析和拓扑学方法，相反，这些领域广泛使用。 此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人学等不同领域都很有用。

Ulrich 9623259 This proposal supports the work of Professor B. Ulrich to work on problems in commutative algebra and algebraic geometry. he intends to study the Rees algebra and its associated graded ring. In particular the proposed research investigates how graded rings associated with an ideal intertwine with the Cohen-Macaulay property. He also intends to study problems that circle around the classical problems of determining the classical join and secant varieties for certain factor rings. Finally, he intends to study the scheme associated to the source and target of finite morphisms between perfect R modules and certain Cohen-Macaulay rings. This research is on the boundary between commutative algebra and algebraic geometry. Both fields arose from the classical problem of studying mathematical objects defined in the plane by the simplest of equations, namely polynomials. Today, the fields use methods not only from algebra, but also from analysis and topology, and conversely are extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.