Quantum Cohomology and Birational Geometry

量子上同调和双有理几何

• 批准号: 0072282
• 负责人: Yongbin Ruan
• 金额: $ 7.5万
• 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: 2000-06-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0072282&HistoricalAwards=false
• 关键词: Quantum; Cohomology; Birational; Geometry

Proposal: DMS-0072282Abstract: Quantum cohomology can be thought of as an algebraic invariant structure of geometric objects called symplectic manifolds. A birational transformation can be thought of as a transformation of a symplectic manifold that is an isomorphism outside of a tiny region where discontinuity can happen. The motivation of this project is the following question: What is the canonical transformation of quantum cohomology? Namely, what kind of transformation of symplectic manifolds will preserve quantum cohomology? The principal investigator's early results indicate that birational transformations may play the role of canonical transformation. This project is devoted to the systematic study of this phenomenon.

提案：DMS-0072282摘要：量子上同调可以被认为是称为辛流形的几何对象的代数不变结构。 双有理变换可以被认为是辛流形的变换，它是可能发生不连续的微小区域之外的同构。 该项目的动机是以下问题：什么是量子上同调的规范变换？ 即，辛流形的什么样的变换将保持量子上同调？ 主要研究者的早期结果表明，双有理变换可能发挥着规范变换的作用。 该项目致力于对这一现象进行系统研究。