Mathematical Sciences: Moduli of Vector Bundles on Surfaces

数学科学：曲面上向量丛的模

• 批准号: 9400835
• 负责人: Kieran O'Grady
• 金额: --
• 依托单位: University of Pennsylvania
• 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: 1994-07-01 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400835&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Moduli; Vector; Bundles

This award supports research in algebraic geometry. There are two objectives of the project. The first is to obtain universal realtions for the values of Donaldson polynomials on classes of algebraic curvs of arbitrary genus and self-intersection. The second is to understand global properties of moduli spaces of bector bundles on surfaces. The 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 ten 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.

该奖项支持代数几何的研究。这个项目有两个目标。首先，得到了任意属自交代数曲线上Donaldson多项式值的一般关系。二是了解曲面上向量束模空间的全局性质。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的十年里，它已经发展到解决了几个世纪以来一直存在的问题的地步。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。