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教授在代数几何学上工作的研究。他将研究光滑的投射品种的基本群体如何影响该空间的生育几何形状。特别是，他想调查基本群体表示空间上的几何条件在多大程度上可以用来证明基本品种的某些生物不变的不变。 这项研究是在代数几何的领域，这是现代数学的最古老部分之一，但它蓬勃发展到过去10年中，它解决了已经存在了几个世纪的问题。最初，它处理了在平面中通过最简单的方程式（即多项式）定义的数字。如今，该领域不仅使用代数的方法，而且使用分析和拓扑的方法，相反，它在这些领域中广泛使用。 此外，它已经证明了自己在物理，理论计算机科学，密码学，编码理论和机器人技术等多样化的领域中有用。