Mathematical Sciences: Research in Commutative Algebra and Invariant Theory

数学科学：交换代数和不变量理论研究

• 批准号: 8903466
• 负责人: Jerzy Weyman
• 金额: --
• 依托单位: Northeastern University
• 依托单位国家: 美国
• 项目类别: Continuing grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903466&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Research; Commutative; Algebra

This project is concerned with research in commutative algebra and invariant theory. The principal investigator intends to find the equations of nilpotent orbits for classical groups and examine Green's conjecture for general canonical curves. In the area of binary forms, he plans to apply his techniques to attack Dixmier's conjecture on systems of parameters for rings of invariants of binary forms. 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.

这个项目是关于交换代数和不变量理论的研究。主要研究人员打算找出经典群的幂零轨道方程，并检验格林关于一般正则曲线的猜想。在二进制形式领域，他计划用他的技术来反驳Dixmier关于二进制形式不变量环的参数系统的猜想。本项目涉及交换代数与代数几何的接口研究。给定一条曲线，一个交换代数可以与它联系在一起。从研究交换代数中得到的信息提供了有关曲线的信息。这是一个发展迅速的领域，对数学的许多领域产生了影响。