The Cohomology Rings of Moduli Spaces

模空间的上同调环

• 批准号: 0432701
• 负责人: C. Clemens
• 金额: --
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2010-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0432701&HistoricalAwards=false
• 关键词: Cohomology; Rings; Moduli; Spaces

DMS-0432701Linda ChenThe investigator will study cohomology rings and Chow rings of various moduli spaces and parameter spaces in algebraic geometry. In particular, she will study Gromov-Witten invariants of toric Deligne-Mumford stacks, (equivariant) cohomology of quot schemes, Chow groups of Fulton-Macpherson spaces, and the birational geometry of moduli spaces of curves. She will also study extensions of Schubert calculus which arise in the study of quantum cohomology. These are distinct projects, but are similar in the fact that each of the spaces involved has a rich combinatorial structure to be analyzed.It is a fundamental problem in algebraic geometry to understand objects satisfying certain geometric criteria, often naturally parametrized by an algebraic scheme or stack. Such moduli and parameter spaces have recently been at the forefront of mathematical and scientific research, much of which has grown out of Kontsevich's introduction of the moduli space of stable maps in the 1990's. They are a source of particular excitement as part of a collision of the fields of algebraic geometry, algebraic combinatorics, symplectic geometry, and theoretical physics.

DMS-0432701 Linda Chen研究者将研究代数几何中各种模空间和参数空间的上同调环和Chow环。 特别是，她将研究Gromov-Witten不变量的环面Deligne-Mumford堆栈，（等变）上同调的quot计划，周群的富尔顿-麦克弗森空间，和双有理几何的模空间的曲线。 她还将研究舒伯特微积分的扩展，这在量子上同调的研究中出现。 这些是不同的项目，但相似之处在于，所涉及的每个空间都有丰富的组合结构需要分析。理解满足某些几何标准的对象是代数几何中的一个基本问题，这些标准通常通过代数方案或堆栈自然参数化。 这样的模和参数空间最近一直处于数学和科学研究的前沿，其中大部分都是从Kontsevich在20世纪90年代引入稳定映射的模空间中发展出来的。 它们是代数几何、代数组合学、辛几何和理论物理领域碰撞的一部分，特别令人兴奋。