Mathematical Sciences: Geometry and Topology

数学科学：几何和拓扑

• 批准号: 9102798
• 负责人: Anatoly Libgober
• 金额: $ 4.82万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1991
• 资助国家: 美国
• 起止时间: 1991-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9102798&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Topology

The investigator will pursue research on various questions concerned with topological properties of algebraic spaces. He intends to study the topology of algebraic varieties, especially invariants of families of plane algebraic curves, invariants of smooth structure on algebraic varieties, and the behavior of complex polynomials near infinity. Relating algebraic to topological structure of spaces is a source of some of the most basic and important questions in mathematics. It calls upon a wide variety of techniques and has challenged major figures in topology and algebra both here and abroad.

研究人员将继续研究与代数空间的拓扑性质有关的各种问题。他打算研究代数簇的拓扑，特别是平面代数曲线族的不变量，代数簇上光滑结构的不变量，以及复多项式在无穷远附近的行为。将代数与空间的拓扑结构联系起来是数学中一些最基本和最重要问题的来源。它需要各种各样的技术，并向国内外拓扑学和代数学的重要人物提出了挑战。