Intersection Theory on Moduli Spaces

这个项目的重点是代数几何中出现的商模空间的交点理论。这包括在向量束的模空间上使用局部化方法来研究曲面不变量，以及计算曲线和向量束的模堆的积分Chow环。我们还考虑了确定哪些堆栈是商堆栈的问题以及奇异商格式的显式Riemann-Roch公式的推导。大部分工作将使用由首席研究员和W. Graham共同开发的等变交集理论。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。

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.