Mathematical Sciences: Linkage, Residual Intersections, and Normal Ideals

数学科学：联系、残差交点和正规理想

• 批准号: 9005873
• 负责人: Bernd Ulrich
• 金额: $ 6.69万
• 依托单位: Michigan State University
• 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: 1990-07-01 至 1993-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9005873&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Linkage; Residual; Intersections

This project is concerned with research in commutative algebra. The principal investigator will determine conditions for an ideal to be in the linkage class of a complete intersection and will show that certain normal ideals are set-theoretic complete intersections. The Cohen-Macaulay property of residual intersections will also be examined. One goal in the study of commutative rings is to classify ideals having certain properties. Many of these results have applications to problems in algebraic geometry. An interesting topic is whether an ideal related by linkage to another ideal shares any of the second ideal's interesting properties, or to what extent it does so. This latter problem is the primary concern of this project.

这个项目是关于交换代数的研究。主要研究人员将确定理想在完全交的联结类中的条件，并将证明某些正规理想是集合论完全交。还将考察剩余交集的Cohen-Macaulay性质。交换环的研究目标之一是对具有某些性质的理想进行分类。这些结果中的许多都应用于代数几何中的问题。一个有趣的话题是，一个通过与另一个理想联系在一起的理想是否共享第二个理想的任何有趣属性，或者在多大程度上这样做。后一个问题是这个项目的主要关注点。