Mathematical Sciences: Curves on Special Surfaces and The Local Miyaoka-Yau Inequality

数学科学：特殊曲面上的曲线和局部 Miyaoka-Yau 不等式

• 批准号: 9302717
• 负责人: Jonathan Wahl
• 金额: $ 7.5万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1993
• 资助国家: 美国
• 起止时间: 1993-07-01 至 1996-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9302717&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Curves; Special; Surfaces

This award supports the research of Professor J. Wahl to work in algebraic geometry. One of the problems that Professor Wahl will address will be studying Gaussian maps on K3 surfaces or more generally on possibly singular surfaces with trivial canonical bundle. He will also continue to study topological properties of local singularities. This research uses the techniques of algebraic geometry, one of the oldest parts of modern mathematics, but one which has had a revolutionary flowering in the past quarter-century. In its origin, it treated figures that could be defined in the plane by the simplest equations, namely polynomials. Nowadays the field makes use of methods not only from algebra, but from analysis and topology, and conversely is finding application in those fields as well as in physics, theoretical computer science, and robotics.

该奖项支持J. Wahl教授在代数几何方面的研究。Wahl教授要解决的问题之一是研究K3曲面上的高斯映射或者更一般地说，研究具有平凡正则束的奇异曲面上的高斯映射。他还将继续研究局部奇点的拓扑性质。这项研究使用了代数几何的技术，这是现代数学中最古老的部分之一，但在过去的四分之一世纪里，它已经有了革命性的发展。在它的起源中，它处理的图形可以用最简单的方程，即多项式，在平面上定义。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，它在这些领域以及物理学、理论计算机科学和机器人技术中也得到了应用。