Gauge Theory and Holomorphic Bundles

规范论和全纯丛

• 批准号: 9703869
• 负责人: Steven Bradlow
• 金额: $ 7.5万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-07-01 至 2000-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9703869&HistoricalAwards=false
• 关键词: Gauge; Theory; Holomorphic; Bundles

9703869 Bradlow This research project lies in the interface of geometry and mathematical physics. More specifically, the investigator is to undertake a systematic study of holomorphic vector bundles equipped with extra structures. Examples of such bundles include Higgs bundles, parabolic bundles, holomorphic pairs, and coherent systems. These bundles have applications in several other branches of mathematics and physics. For example, on a Kahler surface the Seiberg-Witten monopole equations are equivalent to the metric equations for holomorphic pairs on a line bundle. Holomorphic bundles are objects defined over a curved space or a manifold; they have simple local structures allowing algebraic calculations, and when these local calculations are pieced together, they often reveal important geometric properties about the underlying manifold. In recent years holomorphic bundles have played an important role in various parts of mathematics as well as theoretical physics.

小行星9703869 该研究项目处于几何学和数学物理学的结合点。更具体地说，研究者是进行系统的研究配备额外的结构的全纯向量丛。这样的丛的例子包括希格斯丛、抛物丛、全纯对和相干系统。这些丛在数学和物理的其他几个分支中也有应用。例如，在Kahler曲面上的Seiberg-Witten矩阵方程等价于线丛上全纯对的度量方程。 全纯丛是定义在弯曲空间或流形上的对象;它们具有简单的局部结构，允许代数计算，当这些局部计算拼凑在一起时，它们经常揭示关于底层流形的重要几何性质。近年来，全纯丛在数学和理论物理的各个部分都起着重要的作用。