Mathematical Sciences: Vector Bundles and Projective Geometry

数学科学：向量丛和射影几何

• 批准号: 8904243
• 负责人: Lawrence Ein
• 金额: $ 4.05万
• 依托单位: University of Illinois at Chicago
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1989
• 资助国家: 美国
• 起止时间: 1989-07-01 至 1991-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8904243&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Vector; Bundles; Projective

This award supports the research in Algebraic Geometry of Professor Lawrence Ein of the University of Illinois at Chicago. Dr. Ein has several projects, all concerned with the relation between vector bundles and projective geometry. Among these projects are the study of special Cremona transformations, dual varieties and syzygies of the generic canonical curve. This is research in the field 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 theoretical Computer Science and in Robotics.

该奖项支持在代数几何的研究， 位于芝加哥的伊利诺斯大学的劳伦斯·艾恩教授。 Ein博士有几个项目，都与 向量丛和射影几何之间的关系其中 项目是研究特殊克雷莫纳变换，对偶 类属典型曲线的簇和合点。 这是代数几何领域的研究， 现代数学中最古老的部分，但其中有一个 在过去的四分之一个世纪里，革命性的开花。在其 起源，它处理的数字，可以定义在平面上， 最简单的方程，即多项式。如今，该领域 使用的方法不仅从代数，但从分析和 拓扑学，反过来说， 以及理论计算机科学和机器人学。