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教授和R. Varley的研究，以在代数几何形状上工作。 他们将致力于计算地图和奇异性的变形，并将其应用于品种及其模构理论中的问题。 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性的领域中有用。