Some Natural Problems in Complex Geometry

复杂几何中的一些自然问题

• 批准号: 9702836
• 负责人: Stephen S. Yau
• 金额: $ 8.1万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2001-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9702836&HistoricalAwards=false
• 关键词: Some; Natural; Problems; Complex; Geometry

9702836 Yau This project deals with research in complex geometry. More specifically, the investigator is to pursue the classification problem for Cauchy-Riemann manifolds, the complex Plateau problem, and the problem of estimating integral points in tetrahedra. The problem of estimating the number of integer points in tetrahedra has applications in number theory as well as algebraic geometry. In particular, such an estimate can be ussed to find better primality testing and factoring algorithms. The complex Plateau problem is a fundamental problem in complex geometry: it seeks to describe those manifolds that can arise as the boundaries of complex domains.

小行星9702836 这个项目涉及复几何的研究。更具体地说，调查是追求分类问题的柯西-黎曼流形，复杂的高原问题，并估计问题的整数点在四面体。 估计四面体中整数点的个数的问题在数论和代数几何中都有应用。特别是，这样的估计可以用来找到更好的素性测试和因子分解算法。复高原问题是复几何中的一个基本问题：它试图描述那些可以作为复域边界出现的流形。