Toric degenerations and Calabi-Yau orbifolds

环面变性和 Calabi-Yau 眼圈

• 批准号: 165706425
• 负责人: Professor Dr. Helge Ruddat
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2010
• 资助国家: 德国
• 起止时间: 2009-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/165706425?language=en
• 关键词: Toric; degenerations; Calabi; Yau; orbifolds

Since the discovery of canonical smoothing for a degenerate Calabi-Yau manifold by Gross and Siebert in 2007, the scientific program of toric degenerations and affine manifolds has become recognized as the right framework to understand the complex parameter side of the mirror Symmetry of Calabi-Yau manifolds. The proposal concerns important applications of the program to answer cohomological and enumerative questions. I intend to gain an understanding of the role of the Kahler parameters in the conjectural definition of string cohomology and to construct a tropical point of view on conifold transitions. Degenerations of orbifold Calabi-Yau s play an essential role in both of these.

自从2007年Gross和Siebert发现退化的Calabi-Yau流形的正则光滑以来，复曲面退化和仿射流形的科学计划已经被认为是理解Calabi-Yau流形镜像对称的复参数方面的正确框架。该提案涉及的重要应用程序，以回答cohomological和枚举的问题。我打算获得的作用的Kahler参数的弦上同调的代数定义的理解，并构建一个热带的锥型转换的观点。在这两个过程中，眶褶Calabi-Yau的退化都起着重要的作用。