Cohomology of Moduli Spaces

模空间的上同调

• 批准号: GR/T01624/01
• 负责人: Frances Kirwan
• 金额: $ 16.74万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=GR%2FT01624%2F01
• 关键词: Cohomology; Moduli; Spaces

The study of complex algebraic curves, and how they vary in families, has been fundamental to algebraic geometry for at least the last century. Huge advances have been made in recent decades, and unexpected but extremely important links with theoretical physics and other parts of mathematics have been discovered. Nonetheless, in spite of 150 years of investigation, our understanding of the topology of the moduli spaces of curves is still very incomplete. The aim of this project is to gain new understanding of the topology of these and related moduli spaces, and also related moduli spaces of vector bundles over a varying curve, by representing them as quotients in the sense of geometric invariant theory and applying methods developed over the last twenty years for studying such quotients.

至少在上个世纪，对复杂代数曲线及其在家庭中的变化的研究一直是代数几何的基础。近几十年来，已经取得了巨大的进步，并且已经发现了与理论物理学和其他数学部分的意外但极为重要的联系。但是，尽管进行了150年的研究，但我们对曲线模量空间拓扑的理解仍然非常不完整。该项目的目的是通过将它们表示为几何不变理论的人，并应用在过去的二十年中开发的方法来研究这些人，从而使矢量束的拓扑和相关的模量空间具有新的理解，以及相关的矢量捆绑包中相关的模量空间。

项目成果

Geometry of Moduli

模量的几何

• DOI: 10.1007/978-3-319-94881-2_1
• 发表时间: 2018
• 作者: Bérczi G

Quotients of unstable subvarieties and moduli spaces of sheaves of fixed Harder-Narasimhan type

不稳定亚变体的商和固定 Harder-Narasimhan 型滑轮的模空间

• DOI: 10.1112/plms/pds022
• 发表时间: 2012
• 期刊: Proceedings of the London Mathematical Society
• 影响因子: 1.8
• 作者: Hoskins V

Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics

杨米尔斯理论和玉川数：数学中意想不到的联系的魅力

• DOI: 10.1112/blms/bdn036
• 发表时间: 2008
• 期刊: Bulletin of the London Mathematical Society
• 影响因子: 0.9
• 作者: Asok A

A GIT construction of moduli spaces of stable maps in positive characteristic

正特征稳定映射模空间的GIT构造

• DOI: 10.1112/jlms/jdn014
• 发表时间: 2008
• 期刊: Journal of the London Mathematical Society
• 作者: Baldwin E