Mathematical Sciences: Space Curves Which Are the Intersection of Two Surfaces

数学科学：两个曲面相交的空间曲线

• 批准号: 9100983
• 负责人: David Jaffe
• 金额: $ 3.31万
• 依托单位: University of Nebraska-Lincoln
• 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: 1991-09-01 至 1994-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9100983&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Space; Curves; Intersection

This award supports the research of Professor D. Jaffe to work in algebraic geometry. He will work on curves and surfaces in complex projective three-space. In particular, he will work on the conjecture that a smooth connected curve, whose degree exceeds its genus by at least four, is not an intersection of two surfaces. This 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D教授的研究。Jaffe工作 在代数几何中。 他将工作的曲线和曲面， 复射影三维空间 特别是，他将致力于 猜想，一个光滑的连接曲线，其程度超过其 亏格至少四个，不是两个曲面的相交。 这项研究是在代数几何领域，其中之一， 现代数学中最古老的部分，但其中一个蓬勃发展， 在过去的10年里， 已经屹立了几个世纪 最初，它处理的数字定义 用最简单的方程，即多项式。 今天，该领域使用的方法不仅来自代数， 分析和拓扑学，相反，它被广泛用于 这些领域。 此外，它已证明在以下领域是有用的， 包括物理学、理论计算机科学、密码学、 编码理论和机器人学