Mathematical Sciences: Linkage, Residual Intersections, and Normal Ideals

点击翻译按钮获取中文摘要

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.