Mathematical Sciences: Fundamental Groups and Algebraic Geometry

数学科学：基本群和代数几何

• 批准号: 9623184
• 负责人: Donu Arapura
• 金额: $ 5.34万
• 依托单位: Purdue Research Foundation
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-15 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623184&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Fundamental; Groups; Algebraic

Arapura DMS 96-23184 This awards supports the research of Professor D. Arapura to work in algebraic geometry. He will study how the fundamental group of a smooth projective variety affects the birational geometry of the space. In particular, he wants to investigate to what extent geometric conditions on the space of representations of the fundamental group can be used to prove the nonvanishing of certain birational invariants of the underlying variety. This research is in the field of algebraic geometry, one of the oldest parts of modern mathematics, but one which blossomed to the point where it has, in the past 10 years, solved problems that have stood for centuries. Originally, it treated figures defined in the plane by the simplest of equations, namely polynomials. Today, the field uses methods not only from algebra, but also from analysis and topology, and conversely it is extensively used in those fields. Moreover it has proved itself useful in fields as diverse as physics, theoretical computer science, cryptography, coding theory and robotics.

Arapura DMS 96-23184 该奖项支持 D. Arapura 教授在代数几何方面的研究。他将研究平滑射影簇的基本群如何影响空间的双有理几何。特别是，他想研究基本群表示空间上的几何条件在多大程度上可以用来证明基础簇的某些双有理不变量的不消失性。 这项研究属于代数几何领域，代数几何是现代数学最古老的部分之一，但在过去 10 年里蓬勃发展，解决了几个世纪以来一直存在的问题。最初，它处理由最简单的方程（即多项式）在平面中定义的图形。如今，该领域不仅使用代数的方法，还使用分析和拓扑的方法，相反，它在这些领域中得到了广泛的应用。 此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人技术等各个领域都很有用。