Mathematical Sciences: On Several Homological Problems in Commutative Algebra

数学科学：交换代数中的几个同调问题

• 批准号: 9002157
• 负责人: Sankar Dutta
• 金额: $ 4.59万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9002157&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Several; Homological; Problems

This project is concerned with problems in commutative algebra and algebraic geometry. The principal investigator will work on the canonical element conjecture of Hochster and related problems. He will also consider the positivity part of Serre's conjecture on intersection multiplicity of modules. This research is on the interface of algebraic geometry and commutative algebra. This is currently a very active area in which an associated commutative algebra is used to obtain refined knowlege about the underlying geometric object.

该项目涉及交换代数和代数几何中的问题。首席研究员将致力于霍赫斯特规范元素猜想及相关问题的研究。他还将考虑 Serre 关于模块交叉重数的猜想的积极部分。 本研究是代数几何和交换代数的接口。目前这是一个非常活跃的领域，其中使用相关的交换代数来获取有关基础几何对象的精确知识。