Blowing-up Algebras and Residual Intersections

爆炸代数和残差交集

• 批准号: 0070704
• 负责人: Mark Johnson
• 金额: $ 9.12万
• 依托单位: University of Arkansas
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-05-01 至 2003-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0070704&HistoricalAwards=false
• 关键词: Blowing; up; Algebras; Residual; Intersections

This proposal consists of two parts. The first is concerned with thestudy of residual intersections and linkage of ideals. The second isthe investigation of the various associated blowing-up rings. The underlying theme is to explore connections between the two areas. The investigator studies the Cohen-Macaulayness of symmetric algebras, and the normality and the nature of the defining equations of Rees algebras,by utilizing the methods of residual intersections. This project in commutative algebra is motivated by closely related problems in algebraic geometry. The process of blowing-up being a fundamentaltool in study of the singularities of algebraic varieties, our researchof the corresponding algebraic problems will hopefully yield more insight intothe geometry.

该提案由两个部分组成。 第一个关注的是残留的交叉点和理想的联系。 第二个是对各种相关吹动环的调查。 基本主题是探索两个区域之间的联系。研究人员通过利用残留相互切口的方法研究了对称代数的Cohen-Macaulays，以及REES代数定义方程的正态性和性质。 该项目中的该项目是由代数几何形状紧密相关的问题激励的。 在研究代数品种的奇异性研究中，吹吹动的过程是，我们的研究对相应的代数问题的研究将有望产生更多的见解。