Mathematical Sciences: Integrable Systems and Moduli Problems in Algebraic Geometry

数学科学：代数几何中的可积系统和模问题

• 批准号: 8802712
• 负责人: Emma Previato
• 金额: --
• 依托单位: Trustees of Boston University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8802712&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integrable; Systems; Moduli

Emma Previato will continue her research into integrable systems of differential equations and moduli problems in algebraic geometry. She will be studying some of the soliton equations which arise naturally in physics. In particular she will work with the Kadomtsev-Petviashvili equations. These model various standing wave configurations and demonstrate many symmetries. Previato will be investigating the geometrical aspects of this theory. Since the special qualities possessed by these integrable systems are algebraic in nature, her work will have impact in both differential and algebraic geometry. The major objective of the research is to embed integrable systems in moduli spaces in order to gain information on the latter's function theory and properties as projective varieties. This offers potential applications to the study of moduli spaces for vector bundles on curves as well as the possible discovery of some new and interesting finite dimensional integrable systems.

Emma Previato将继续她对可积微分方程组和代数几何中的模问题的研究。她将研究物理学中自然产生的一些孤子方程。特别是，她将研究Kadomtsev-Petviashvili方程。它们模拟了各种驻波结构，并展示了许多对称性。普雷维亚托将研究这一理论的几何方面。由于这些可积系统所具有的特殊性质本质上是代数的，她的工作将对微分几何和代数几何产生影响。研究的主要目的是将可积系统嵌入到模空间中，以获得关于后者的函数理论和作为射影簇的性质的信息。这为研究曲线上向量丛的模空间以及发现一些新的有趣的有限维可积系统提供了潜在的应用。