Recursive formulas for Gromov-Witten invariants

Gromov-Witten 不变量的递归公式

基本信息

批准号：
0071393
负责人：
Eleny-Nicoleta Ionel
金额：
$ 5.87万
依托单位：
University of Wisconsin-Madison
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2000
资助国家：
美国
起止时间：
2000-06-01 至 2003-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071393&HistoricalAwards=false
关键词：
Recursive formulas Gromov Witten invariants

项目摘要

Award: DMS-0071393Principal Investigator: Eleny-Nicoleta IonelThe goal of the first project is to obtain new relations in thecohomology of the moduli space of complex structures on a markedRiemann surface. Using techniques developed in her earlier work,the PI found several interesting relations, one of which couldprove the Faber conjecture about the generators of thetautological ring. The second project seeks to find relationsbetween the relative and absolute Gromov-Witten invariants. Suchrelations appear to be useful in mirror conjecture computations,as well as in several other open problems in enumerativegeometry. The final project suggests two ways of extending theGromov-type invariants to `nongeneric' situations. This wouldprovide more refined information about the symplectic manifold. Most of the problems in enumerative algebraic geometry are morethan a hundred years old. The questions are easy to ask, but theprogress in solving them using classical methods has been quiteslow. Recently, the same kind of questions arised in twodimensional topological quantuum field theories from high energyphysics. Inspired by these theories, new methods lead in the pastcouple of years to amazing progress in the field. The proposalexplores two new ways of approaching these old problems thatwould further clarify the structure of the two dimensionaltopological quantuum field theories.

奖项：DMS-0071393 首席研究员：Eleny-Nicoleta Ionel 第一个项目的目标是在标记黎曼曲面上的复杂结构的模空间的上同调中获得新的关系。使用她早期工作中开发的技术，PI 发现了几个有趣的关系，其中之一可以证明关于同义反复环的生成器的费伯猜想。第二个项目旨在寻找相对和绝对 Gromov-Witten 不变量之间的关系。这种关系似乎在镜像猜想计算以及枚举几何中的其他几个开放问题中很有用。最终项目提出了两种将格罗莫夫型不变量扩展到“非泛型”情况的方法。这将提供有关辛流形的更精确的信息。枚举代数几何中的大多数问题都有一百多年的历史了。这些问题很容易提出，但使用经典方法解决这些问题的进展却相当缓慢。最近，高能物理学的二维拓扑量子场论也出现了同样的问题。受这些理论的启发，新方法在过去几年中在该领域取得了惊人的进展。该提案探索了解决这些老问题的两种新方法，这将进一步阐明二维拓扑量子场论的结构。