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教授的研究。史密斯和 R.瓦利在代数几何工作。 他们将致力于 计算地图和奇点的变形并应用它 在霍奇结构理论的问题，品种和 他们的模量。 这项研究是在代数几何领域，其中一个 现代数学中最古老的部分，但其中一个 在过去的10年里， 已经屹立了几个世纪 最初，它把数字 在平面上由最简单的方程定义，即 多项式 今天，该领域使用的方法不仅来自 代数，但也从分析和拓扑学，反过来说，它 广泛应用于这些领域。 此外，它还证明， 它本身在物理学、理论、 计算机科学、密码学、编码理论和机器人技术。