Mathematical Sciences: Studies in Algebraic Geometry

数学科学：代数几何研究

• 批准号: 9623041
• 负责人: Igor Dolgachev
• 金额: $ 6.75万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1996
• 资助国家: 美国
• 起止时间: 1996-09-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9623041&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Studies; Algebraic; Geometry

The investigator studies arithmetical group quotients of bounded Hermitian domains of exceptional types with the goal to find their geometric interpretation as the moduli spaces of some special Calabi-Yau manifolds. The cohomology of such varieties should carry additional special structures related to representation theory of Lie groups of exceptional type. Calabi-Yau manifolds have recently become notorious because of their important role in physics. New ten dimensional models of the space-time proposed in the string theory contain a Calabi-Yau manifold as an additional part to the usual four dimensional space-time. The special Calabi-Yau manifolds sought by the investigator may appear as the right candidates for the choice of the model of the space-time.

研究了特殊类型的有界Hermitian域的算术群代数，目的是找到它们作为某些特殊Calabi-Yau流形的模空间的几何解释。这些变种的上同调应该带有额外的特殊结构，与例外类型李群的表示论有关。 卡-丘流形最近因为其在物理学中的重要作用而变得臭名昭著。弦理论中提出的新的十维时空模型包含一个卡-丘流形，作为通常四维时空的附加部分。研究者所寻找的特殊卡-丘流形可能是选择时空模型的正确候选者。