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.

卡特科斯基提议研究涉及代数几何和交换代数相互作用的几个问题。 将研究高次理想的渐近性质。 良好的稳定性能往往适用于高功率。将研究代数簇映射的环形化，继续 PI 之前的工作。 将研究积极特征品种的分支，着眼于局部统一。作者将研究诺特环上的估价半群的分类以及估价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。 卡特科斯基将研究代数中几个具有理论重要性的问题。 通过该项目，本科生和研究生将接受培训，年轻的研究人员将得到指导。