Mathematical Sciences: Geometry of Period Mappings and Abelian Varieties

数学科学：周期映射几何和阿贝尔簇

• 批准号: 9208282
• 负责人: Roy Smith
• 金额: $ 5.72万
• 依托单位: University of Georgia Research Foundation Inc
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-15 至 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9208282&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Period; Mappings

This awards supports the research of Professors R. Smith and R. Varley to work in algebraic geometry. They will work on computing deformations of maps and singularities and applying it to problems in the theory of Hodge structures of varieties and their moduli. 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 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.

该奖项支持 R. Smith 和 R. Varley 教授在代数几何方面的研究。 他们将致力于计算图和奇点的变形，并将其应用于簇及其模的霍奇结构理论中的问题。 这项研究属于代数几何领域，它是现代数学最古老的部分之一，但在过去十年里蓬勃发展，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。