Mathematical Sciences: Hodge Theory

数学科学：霍奇理论

• 批准号: 8801430
• 负责人: Aroldo Kaplan
• 金额: $ 15.34万
• 依托单位: University of Massachusetts Amherst
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-06-01 至 1992-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8801430&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hodge; Theory

Eduardo Cattani and Aroldo Kaplan will continue their work in Hodge theory. This involves the study of topological and geometric invariants connected with an algebraic variety. Hodge theory yields a method of describing the space of differential forms on a manifold. This theory has seen very rapid developments in recent years. Most notably, on the construction of functorial Hodge structures on appropriate cohomology and homotopy spaces. The work of Cattani and Kaplan in cooperation with Wilfried Schmid has been at the forefront of research in variations of Hodge structures. Cattani and Kaplan will build on their recent results which bring the several variable case within reach of applications. They will apply these results to the study of the behaviour of integral cycles in an algebraic family of varieties. They will also study the structure of modular varieties. This work will focus on the characterization of maximal integral submanifolds for the horizontal distribution in a classifying space for Hodge structures.

Eduardo Cattani和Aroldo Kaplan将继续他们的工作 霍奇理论这涉及到拓扑学的研究， 与代数簇有关的几何不变量。霍奇 理论产生了一种描述微分空间的方法， 在流形上形成。这一理论的发展非常迅速 近年来最值得注意的是，在构造函式时， 适当的上同调与同伦空间上的霍奇结构。 Cattani和Kaplan与Wilfried合作的工作 施密德一直处于研究的最前沿， 霍奇建筑。 Cattani和Kaplan将在他们最近的研究结果的基础上， 使几种变量的情况在应用范围内。 他们将把这些结果应用于研究 代数簇族中的整圈。他们将 还研究了模块化品种的结构。这项工作将 重点讨论了极大积分子流形的特征 对于Hodge在分类空间中的水平分布， 结构.