Intersection Theory on Moduli Spaces

模空间的交集理论

• 批准号: 9870033
• 负责人: Dan Edidin
• 金额: $ 6.35万
• 依托单位: University of Missouri-Columbia
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-09-01 至 2003-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9870033&HistoricalAwards=false
• 关键词: Intersection; Theory; Moduli; Spaces

9870033 Edidin The focus of this project is intersection theory on quotient moduli spaces that arise in algebraic geometry. This includes using localization methods on moduli spaces of vector bundles to study surface invariants, as well as calculating integral Chow rings of moduli stacks of curves and vector bundles. We also consider the problems of determining which stacks are quotient stacks and of obtaining an explicit Riemann-Roch formula for singular quotient schemes. Much of the work will use the equivariant intersection theory developed jointly by the principal investigator and W. Graham. This is research in the field of algebraic geometry. Algebraic geometry 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.

小行星9870033 这个项目的重点是在代数几何中出现的商模空间的交集理论。这包括使用向量丛模空间上的局部化方法来研究曲面不变量，以及计算曲线和向量丛模堆叠的积分Chow环。我们还考虑的问题，确定哪些堆栈是商栈，并获得一个明确的Riemann-Roch公式奇异商计划。 大部分工作将使用由首席研究员和W.格雷姆 这是代数几何领域的研究。 代数几何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。在其起源，它处理的数字，可以定义在平面上的最简单的方程，即多项式。如今，该领域不仅使用代数方法，还使用分析和拓扑学方法，相反，这些方法在这些领域以及物理学，理论计算机科学和机器人学中也得到了应用。