Mathematical Sciences: Moduli Problems in Algebraic Geometry

数学科学：代数几何中的模问题

• 批准号: 9500964
• 负责人: Michael Thaddeus
• 金额: $ 4.5万
• 依托单位: Harvard University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500964&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Moduli; Problems; Algebraic

9500964 Thaddeus Professor Thaddeus will study the topology and geometry of quotient varieties using his techniques of flips. In particular he will study configuration spaces of certain projective spaces. He will also study moduli spaces off vector bundles and curves. he hopes to compute relations in their cohomology rings and the associated Hilbert polynomials. This is research in the field of algebraic geometry, yet it directly connects to two of the great advances in theoretical physics in this century--quantum mechanics and general relativity. Algebraic geometry itself is 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. ***

9500964 Thaddeus教授将使用他的掷硬币技术来研究商变的拓扑和几何。特别是他将研究某些射影空间的构形空间。他还将研究矢量束和曲线的模空间。他希望计算它们的上同调环中的关系和相关的希尔伯特多项式。这是代数几何领域的研究，但它直接关系到本世纪理论物理学的两大进步——量子力学和广义相对论。代数几何本身是现代数学中最古老的部分之一，但在过去的四分之一个世纪里，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。＊＊＊