Mathematical Sciences: Gaussian Maps and Topology of ComplexSurface Singularities

数学科学：高斯图和复杂表面奇点的拓扑

• 批准号: 9103604
• 负责人: Jonathan Wahl
• 金额: $ 6.44万
• 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: 1991
• 资助国家: 美国
• 起止时间: 1991-06-15 至 1994-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9103604&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Gaussian; Maps; Topology

This award supports the research of Professor J. Wahl to work in algebraic geometry. He will study the Gaussian map in different situations. Along with his graduate students, he intends to study the stratification of the moduli space of curves of genus g by the corank of the Gaussian map of the canonical bundle. 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J. Wahl教授在代数几何方面的研究。他将研究不同情况下的高斯图。与他的研究生一起，他打算通过正则束的高斯映射的corank来研究g属曲线的模空间的分层。这项研究是在代数几何领域进行的，代数几何是现代数学中最古老的部分之一，但在过去的10年里，它已经发展到解决了几个世纪以来一直存在的问题的程度。最初，它用最简单的方程，即多项式来处理平面上定义的图形。今天，该领域不仅使用代数的方法，而且还使用分析和拓扑的方法，相反，它在这些领域中被广泛使用。此外，它已被证明在物理学、理论计算机科学、密码学、编码理论和机器人等多种领域都很有用。