Mathematical Sciences: Free Resolutions in Commutative Algebra

数学科学：交换代数的自由解析

• 批准号: 9322556
• 负责人: Andrew Kustin
• 金额: $ 5万
• 依托单位: University of South Carolina at Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-01 至 1997-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9322556&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Free; Resolutions; Commutative

This award supports research on free resolutions in commutative algebra. The principal investigator will study a conjecture of Vasconcelos, the Poincare series and asymptotic behavior of betti numbers of modules over rings with small linking number, higher order multiplication in Tor-algebras, and the cokernel of generic exterior multiplication. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.

该奖项支持交换代数中自由解析的研究。 首席研究员将研究 Vasconcelos 猜想、庞加莱级数、小连接数环上模贝蒂数的渐近行为、Tor 代数中的高阶乘法以及泛型外乘法的 cokernel。 这项研究涉及交换代数和代数几何中的许多问题。 代数几何研究多项式方程族的解。 人们可以研究解集的几何形状，也可以通过研究解集上形成所谓交换环的某些函数来用代数方法解决问题。 这种双重视角在交换代数和代数几何之间建立了紧密的联系。