Mathematical Sciences: Hodge Structures and L2 Cohomology

数学科学：Hodge 结构和 L2 上同调

• 批准号: 9505040
• 负责人: Mark Stern
• 金额: $ 7.5万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-06-15 至 1999-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9505040&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Hodge; Structures; L2

9505040 Stern The proposed research has to do with the Hodge theory of singular or noncompact varieties. The investigator proposes to realize the intersection cohomology of a projective variety as an explicit complex of differential forms equipped with a Hodge filtration. He also proposes to construct harmonic automorphic representatives of de Rham cohomology classes of locally symmetric spaces. Varieties are a central object in geometry and algebra as they arise as solutions to polynomial equations in various dimensions. Intersection cohomology is a way to understand how these varieties are situated in space by looking at their various intersection properties.

9505040斯特恩拟议的研究与奇异或非紧致变种的霍奇理论有关。研究者建议将射影簇的交上同调实现为带有Hodge滤子的显式微分形式复形。他还建议构造局部对称空间的de Rham上同调类的调和自同构表示。变数是几何学和代数学中的一个中心对象，因为它们作为不同维度的多项式方程的解而出现。交上同调是一种通过观察它们的各种交集性质来理解这些变体如何位于空间中的方法。