Mathematical Sciences: Problems in Algebraic Geometry

数学科学：代数几何问题

• 批准号: 8902251
• 负责人: Robert Lazarsfeld
• 金额: $ 33.59万
• 依托单位: University of California-Los Angeles
• 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 1995-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8902251&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Problems; Algebraic; Geometry

This award supports the research in Algebraic Geometry of Professor Robert Lazarsfeld of the University of California at Los Angeles. Dr. Lazarsfeld will be continuing his work on the applications of vector bundle techniques in the study of linear series. In particular, he intends to investigate some problems involving the Noether-Lefschetz locus as well as some questions arising out of work already begun with Dr. Mark Green of UCLA, on generic vanishing theorems. 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.

该奖项支持加州大学洛杉矶分校罗伯特·拉扎斯菲尔德教授的代数几何研究。 Lazarsfeld 博士将继续致力于矢量丛技术在线性级数研究中的应用。特别是，他打算研究涉及 Noether-Lefschetz 轨迹的一些问题，以及由加州大学洛杉矶分校的 Mark Green 博士已经开始的关于泛型消失定理的工作中产生的一些问题。 这是代数几何领域的研究，代数几何是现代数学最古老的部分之一，但在过去四分之一个世纪中取得了革命性的繁荣。在它的起源中，它处理可以通过最简单的方程（即多项式）在平面上定义的图形。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，它正在这些领域以及理论计算机科学和机器人技术中找到应用。