Mathematical Sciences: Geometry of Period Mappings and Abelian Varieties

数学科学：周期映射几何和阿贝尔簇

• 批准号: 8803487
• 负责人: Roy Smith
• 金额: $ 8.16万
• 依托单位: University of Georgia Research Foundation Inc
• 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: 1988-07-01 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8803487&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Geometry; Period; Mappings

This research will be in algebraic geometry, especially the study of geometrically defined subvarieties of moduli spaces of curves, hypersurfaces, and abelian varieties, and of more general period spaces, and applications to period maps. In particular they plan to extend their analysis of the geometry of discriminant loci for families of hypersurfaces to mappings and families of algebraic cycles. One principal application will be to the study of the Hodge problem for one cycles on projective threefolds and two-cycles on abelian varieties.

这项研究将在代数几何，特别是 模空间的几何定义子簇的研究 曲线、超曲面和阿贝尔变体，以及更一般的 周期空间，以及周期映射的应用。 特别是 他们计划扩展他们的几何分析， 映射的超曲面族的判别轨迹 代数圈族 一个主要应用将是 关于射影空间上单圈的Hodge问题的研究 三倍和两个循环的阿贝尔变种。