Singularity Theory and Commutative Algebra

奇点理论和交换代数

• 批准号: 1064425
• 负责人: Steven Cutkosky
• 金额: $ 21.8万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-01 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1064425&HistoricalAwards=false
• 关键词: Singularity; Theory; Commutative; Algebra

Cutkosky proposes to investigate several problems involving the interaction of algebraic geometry and commutative algebra. Asymptotic properties of high powers of ideals will be investigated. Good stable properties tend to hold for high powers. Toroidalization of mappings of algebraic varieties will be studied, continuing previous work of the PI. Ramification of varieties in positive characteristic will be investigated, with an eye towards local uniformization. The author will investigate the related problem of classification of semigroups of valuations on a noetherian ring, and the construction of generating sequences of valuations.Algebra is of increasing importance in modern science and technology. Cutkosky will investigate several problems of theoretical importance in algebra. Undergraduate and graduate students will be trained and young researchers will be mentored through this project.

Cutkosky建议调查几个问题，涉及代数几何和 交换代数 将研究理想的高次幂的渐近性质。 良好的稳定性能往往适用于高功率。代数簇映射的环面化将被研究，继续PI以前的工作。 品种的分枝在积极的特点将进行调查，着眼于当地的统一。本文研究了Noether环上赋值半群的分类和赋值生成序列的构造等相关问题。代数在现代科学技术中的重要性与日俱增。 Cutkosky将调查几个问题的理论重要性代数。 本科生和研究生将接受培训，年轻的研究人员将通过这个项目得到指导。