Research in Commutative Algebra

交换代数研究

• 批准号: 0099415
• 负责人: Irena Peeva
• 金额: $ 10.26万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-07-15 至 2004-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0099415&HistoricalAwards=false
• 关键词: Research; Commutative; Algebra

This project deals with the structure of minimal free resolutions and their applications in algebraic geometry. The P.I. will conduct research on the following topics : 1) connectedness and smoothness of Hilbert schemes over exterior algebras (joint with M. Stillman); 2) the asymptotic properties and structure of free resolutions over complete intersections; 3) free resolutions over rings with restricted powers (joint with V. Gasharov and T. Hibi).The proposed research is in the closely related fields of commutative algebra and algebraic geometry. These fields study the algebraic invariants of systems of polynomial equations and the geometry of sets defined by the vanishing of polynomials. Usually it is very difficult to find explicitly the solutions of a system of polynomial equations; however one can study the geometric properties of the set of solutions. Some of the results in these fields have applications in communications and robotics.

本课题研究最小自由分辨率的结构及其在代数几何中的应用。P.I.将研究以下问题：1)外代数上Hilbert格式的连通性和光滑性(与M.Stillman合作)；2)完全交上自由分解的渐近性质和结构；3)有限幂环上的自由分解(与V.Gasharov和T.Hibi联合)。建议的研究是在交换代数和代数几何密切相关的领域。这些领域研究多项式方程组的代数不变量和由多项式的消失所定义的集合的几何。通常很难显式地求出多项式方程组的解，但人们可以研究该解集的几何性质。这些领域的一些成果在通信和机器人领域都有应用。